2005年 第31卷 第3期
2005, 31(3): 335-342.
摘要:
Decentralized closed-loop identification and controller design for a kind of cascade processes composed of several sub-processes are studied. There are only input couplings between adjacent sub-processes. First, the cascade process is divided into several two-input two-output systems and coupling models of adjacent sub-processes are obtained via decentralized identification. TITO sys- tem is decoupled equivalently into four independent single open-loop processes with the same input signal. Then, a distributed model predictive control algorithm is proposed based on the coupling models of adjacent sub-processes.
Decentralized closed-loop identification and controller design for a kind of cascade processes composed of several sub-processes are studied. There are only input couplings between adjacent sub-processes. First, the cascade process is divided into several two-input two-output systems and coupling models of adjacent sub-processes are obtained via decentralized identification. TITO sys- tem is decoupled equivalently into four independent single open-loop processes with the same input signal. Then, a distributed model predictive control algorithm is proposed based on the coupling models of adjacent sub-processes.
2005, 31(3): 343-351.
摘要:
This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems. At first, a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudoweights is introduced. The new model is then compared with the existing B-spline models in terms of feasible domains. Next, a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available. Finally, illustrative examples indicate the effectiveness of the proposed algorithms.
This paper presents a new method for the modeling and control of the output probability density functions (PDFs) of linear stochastic systems. At first, a new PDF approximation method, namely the rational square-root B-spline model is proposed and the innovative concept of pseudoweights is introduced. The new model is then compared with the existing B-spline models in terms of feasible domains. Next, a controller is developed to realize the output PDF tracking performance. An alternative minimal entropy control strategy is also provided for the case that no target PDF is available. Finally, illustrative examples indicate the effectiveness of the proposed algorithms.
2005, 31(3): 352-358.
摘要:
This paper deals with a general class of optimization problems in robust control with given expectation value of performance index, which can be transformed into the problem of matrix approximation with matrix inequalities constraints. Theorem for existence and the uniqueness of the solutions of matrix approximation with linear matrix inequalities (LMIs) constraints is presented and algorithms for solving the problems of matrix approximation with matrix inequalities constraints are given based on the fact that such problems can be converted into the generalized eigenvalue problem (GEVP) of LMI. Examples are given to illustrate the main results of the paper.
This paper deals with a general class of optimization problems in robust control with given expectation value of performance index, which can be transformed into the problem of matrix approximation with matrix inequalities constraints. Theorem for existence and the uniqueness of the solutions of matrix approximation with linear matrix inequalities (LMIs) constraints is presented and algorithms for solving the problems of matrix approximation with matrix inequalities constraints are given based on the fact that such problems can be converted into the generalized eigenvalue problem (GEVP) of LMI. Examples are given to illustrate the main results of the paper.
2005, 31(3): 359-364.
摘要:
Robot navigation based on character recognition is an effective vision method for compensating the disadvantage of ultrasonic and infrared sensors. A typical example of character recognition for mobile robot navigation is the doorplate recognition system. The captured doorplate images contain unexpected noise from irregular illumination conditions, various imaging angles, different imaging distances, etc. The unexpected noise may still exist after segmentation step. In this paper, a robust segmentation method based on speculating the candidates of the characters and feeding back the classification result to the segmentation process is presented. If the candidates of doorplate characters cannot be determined at the segmentation step, a speculation according to known knowledge is executed. The threshold for character extraction from candidates is adjusted when the corresponding character is rejected after classification. The experimental results indicate that the recognition results are effectively improved with the proposed segmentation method.
Robot navigation based on character recognition is an effective vision method for compensating the disadvantage of ultrasonic and infrared sensors. A typical example of character recognition for mobile robot navigation is the doorplate recognition system. The captured doorplate images contain unexpected noise from irregular illumination conditions, various imaging angles, different imaging distances, etc. The unexpected noise may still exist after segmentation step. In this paper, a robust segmentation method based on speculating the candidates of the characters and feeding back the classification result to the segmentation process is presented. If the candidates of doorplate characters cannot be determined at the segmentation step, a speculation according to known knowledge is executed. The threshold for character extraction from candidates is adjusted when the corresponding character is rejected after classification. The experimental results indicate that the recognition results are effectively improved with the proposed segmentation method.
2005, 31(3): 365-371.
摘要:
Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form. For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissipative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties. The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H1 control and positive real control and provide a more flexible and less conservative control design method.
Robust quadratic dissipative control for a class of linear multi-variable systems with parameter uncertainties is considered, where the uncertainties are expressed in a linear fractional form. For the nominal system without uncertainties, the equivalence between quadratic dissipativeness and positive realness is established, and conditions are derived for linear systems to be quadratic dissipative. As for uncertain systems, it is shown that the robust quadratic dissipative control problem for the uncertain system can be reduced to the corresponding problem for a related system without uncertainties. The control problem concerned can be solved using LMI approach. The results of the paper unify existing results on H1 control and positive real control and provide a more flexible and less conservative control design method.
2005, 31(3): 372-378.
摘要:
Two kinds of observers for linear singular time-delay systems, namely functional observers and full-order observers, are considered in this paper. For the former, observers with and without internal delay are considered. For the latter, observers without internal delay is given. The corresponding design steps for various observers, which are all normal linear time-delay systems, are presented. Numerical examples are given to illustrate the methods.
Two kinds of observers for linear singular time-delay systems, namely functional observers and full-order observers, are considered in this paper. For the former, observers with and without internal delay are considered. For the latter, observers without internal delay is given. The corresponding design steps for various observers, which are all normal linear time-delay systems, are presented. Numerical examples are given to illustrate the methods.
2005, 31(3): 379-384.
摘要:
A necessary and sufficient condition of the quadratic D-stability for a class of uncertain linear systems is presented in terms of linear matrix inequality (LMI) technology. Finally, the validity and less conservatism of the obtained results in this paper are illustrated by a benchmark example.
A necessary and sufficient condition of the quadratic D-stability for a class of uncertain linear systems is presented in terms of linear matrix inequality (LMI) technology. Finally, the validity and less conservatism of the obtained results in this paper are illustrated by a benchmark example.
2005, 31(3): 385-393.
摘要:
This paper addresses the problem of dynamic multiscale system (DMS) estimation. Research achievements in the related area have been reported in the literature, but they either rely on the assumption of stationarity of the observed process or are difficult to be implemented. In this paper, a model of DMS that meets the requirements of the standard discrete time Kalman filtering is built and is realized by general compactly supported wavelet. The introduction of the state space projection equation and the augmentation of measurement equation are a major part of the novelty in our work. A theorem on the optimal filtering output at each scale is put forward. Experimental results are given to verify our methods0 superior performances.
This paper addresses the problem of dynamic multiscale system (DMS) estimation. Research achievements in the related area have been reported in the literature, but they either rely on the assumption of stationarity of the observed process or are difficult to be implemented. In this paper, a model of DMS that meets the requirements of the standard discrete time Kalman filtering is built and is realized by general compactly supported wavelet. The introduction of the state space projection equation and the augmentation of measurement equation are a major part of the novelty in our work. A theorem on the optimal filtering output at each scale is put forward. Experimental results are given to verify our methods0 superior performances.
2005, 31(3): 394-401.
摘要:
This paper develops fuzzy H1 filter for state estimation approach for nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. We design a stable fuzzy H1 filter based on the Takagi-Sugeno (T-S) fuzzy model, which assures asymptotic stability and a prescribed H1 index for the filtering error system. Sufficient condition for the existence of such a filter is established by solving the linear matrix inequality (LMI) problem. The LMI problem can be efficiently solved with global convergence using the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the proposed method.
This paper develops fuzzy H1 filter for state estimation approach for nonlinear discrete-time systems with multiple time delays and unknown bounded disturbances. We design a stable fuzzy H1 filter based on the Takagi-Sugeno (T-S) fuzzy model, which assures asymptotic stability and a prescribed H1 index for the filtering error system. Sufficient condition for the existence of such a filter is established by solving the linear matrix inequality (LMI) problem. The LMI problem can be efficiently solved with global convergence using the interior point algorithm. Simulation examples are provided to illustrate the design procedure of the proposed method.
2005, 31(3): 402-405.
摘要:
The camera resection and the PnP problem are both of great importance in computer vision field. However, these two fundamentally different problems are often mistaken one another in the literature. In this short note, the essential differences of these two problems are clarified, and such a clarification seems helpful for those who are working on the problems.
The camera resection and the PnP problem are both of great importance in computer vision field. However, these two fundamentally different problems are often mistaken one another in the literature. In this short note, the essential differences of these two problems are clarified, and such a clarification seems helpful for those who are working on the problems.
2005, 31(3): 406-411.
摘要:
The reliability analysis of a system with repairable failures and non-repairable failures is presented. It is assumed that the system has n repairable failure modes and m non-repairable failure modes. As one repairable failure mode takes place, the system will be repaired after the failure mode is detected, otherwise, it would never work again when attaining one non-repairable failure mode. Thus, the system brings about new reliability indices for having both repairable failures and non-repairable failures. The definitions of the new reliability indices are given, and the calculating methods for them are derived by using probability analysis and the supplementary variable technique.
The reliability analysis of a system with repairable failures and non-repairable failures is presented. It is assumed that the system has n repairable failure modes and m non-repairable failure modes. As one repairable failure mode takes place, the system will be repaired after the failure mode is detected, otherwise, it would never work again when attaining one non-repairable failure mode. Thus, the system brings about new reliability indices for having both repairable failures and non-repairable failures. The definitions of the new reliability indices are given, and the calculating methods for them are derived by using probability analysis and the supplementary variable technique.
2005, 31(3): 412-418.
摘要:
A global relay switching control scheme with finite time convergence (FTC) is proposed for multi-joint rigid robotic manipulator systems with uncertain dynamics. For a general finite time controller, the control signals may tend to infinity in finite time when the initial states of the system are in some specified area, causing the singularity problem of the closed-loop system and finite escape. The design scheme for finite time tracking control uses a relay switching control method so that the boundedness of the control signal is guaranteed and the singularity phenomenon is avoided. The validity of our scheme is demonstrated by simulation results.
A global relay switching control scheme with finite time convergence (FTC) is proposed for multi-joint rigid robotic manipulator systems with uncertain dynamics. For a general finite time controller, the control signals may tend to infinity in finite time when the initial states of the system are in some specified area, causing the singularity problem of the closed-loop system and finite escape. The design scheme for finite time tracking control uses a relay switching control method so that the boundedness of the control signal is guaranteed and the singularity phenomenon is avoided. The validity of our scheme is demonstrated by simulation results.
2005, 31(3): 419-426.
摘要:
A successive approximation approach for designing optimal controllers is presented for discrete linear time-delay systems with a quadratic performance index. By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. The optimal control law obtained consists of an accurate feedback terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint equations. By using a finite-step iteration of the time-delay compensation term of the optimal solution sequence, a suboptimal control law is obtained. Simulation examples are employed to test the validity of the proposed approach.
A successive approximation approach for designing optimal controllers is presented for discrete linear time-delay systems with a quadratic performance index. By using the successive approximation approach, the original optimal control problem is transformed into a sequence of nonhomogeneous linear two-point boundary value (TPBV) problems without time-delay and time-advance terms. The optimal control law obtained consists of an accurate feedback terms and a time-delay compensation term which is the limit of the solution sequence of the adjoint equations. By using a finite-step iteration of the time-delay compensation term of the optimal solution sequence, a suboptimal control law is obtained. Simulation examples are employed to test the validity of the proposed approach.
2005, 31(3): 427-433.
摘要:
A fast object detection method based on object region dissimilarity and 1-D AGADM (one dimensional average gray absolute difference maximum) between object and background is proposed for real-time defection of small offshore targets. Then computational complexity, antinoise performance, the signal-to-noise ratio (SNR) gain between original images and their results as a function of SNR of original images and receiver operating characteristic (ROC) curve are analyzed and compared with those existing methods of small target detection such as two dimensional average gray absolute difference maximum (2-D AGADM), median contrast filter algorithm and multi-level filter algorithm. Experimental results and theoretical analysis have shown that the proposed method has faster speed and more adaptability to small object shape and also yields improved SNR performance.
A fast object detection method based on object region dissimilarity and 1-D AGADM (one dimensional average gray absolute difference maximum) between object and background is proposed for real-time defection of small offshore targets. Then computational complexity, antinoise performance, the signal-to-noise ratio (SNR) gain between original images and their results as a function of SNR of original images and receiver operating characteristic (ROC) curve are analyzed and compared with those existing methods of small target detection such as two dimensional average gray absolute difference maximum (2-D AGADM), median contrast filter algorithm and multi-level filter algorithm. Experimental results and theoretical analysis have shown that the proposed method has faster speed and more adaptability to small object shape and also yields improved SNR performance.
2005, 31(3): 434-439.
摘要:
Consistency and the weights estimation model of the interval number comparison matrix (INCM) in the analytical hierarchy process is studied under uncertainty decision-making case. Based on the weights feasible region, the local consistency definition and the local satisfactory consistency definition are given. Then, a computational model set up to test whether the INCM has the local satisfactory consistency or not. Moreover, the consistency degree based on the random crisp comparison matrix is defined as an effective index to test the consistency. Next, the upper range model, the lower range model, and the possible value model are put forward which can solve the problem that some existing approaches do not consider the consistency and its effect on the weights. According to the property of these models, a genetic algorithm is developed.
Consistency and the weights estimation model of the interval number comparison matrix (INCM) in the analytical hierarchy process is studied under uncertainty decision-making case. Based on the weights feasible region, the local consistency definition and the local satisfactory consistency definition are given. Then, a computational model set up to test whether the INCM has the local satisfactory consistency or not. Moreover, the consistency degree based on the random crisp comparison matrix is defined as an effective index to test the consistency. Next, the upper range model, the lower range model, and the possible value model are put forward which can solve the problem that some existing approaches do not consider the consistency and its effect on the weights. According to the property of these models, a genetic algorithm is developed.
2005, 31(3): 440-445.
摘要:
The data packet dropouts phenomenon is usually inevitable when information transmitted among communication networks. In this paper, the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied. First, an uncertain discrete-time switching system model is presented to describe these networked control systems. The stability equivalence is then proved between this switching system and an uncertain impulsive difference system. Moreover, a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system. From this condition the robust stabilization problem is dealt with for the uncertain impulsive system. Main results are given in linear matrix inequalities. Finally a numerical example is given to illustrate the theoretical results.
The data packet dropouts phenomenon is usually inevitable when information transmitted among communication networks. In this paper, the robust stabilization problem for uncertain networked control systems with data packet dropouts is studied. First, an uncertain discrete-time switching system model is presented to describe these networked control systems. The stability equivalence is then proved between this switching system and an uncertain impulsive difference system. Moreover, a sufficient condition is obtained for the asymptotical stability of the nonlinear impulsive difference system. From this condition the robust stabilization problem is dealt with for the uncertain impulsive system. Main results are given in linear matrix inequalities. Finally a numerical example is given to illustrate the theoretical results.
2005, 31(3): 446-450.
摘要:
The paper is concerned with the robust control problems for exponential controlled closed queuing networks (CCQNs) under uncertain routing probabilities. As the rows of some parameter matrices such as infinitesimal generators may be dependent, we first transform the objective vector under discounted-cost criteria into a weighed-average cost. Through the solution to Poisson equation, i.e., Markov performance potentials, we then unify both discounted-cost and average-cost problems to study, and derive the gradient formula of the new objective function with respect to the routing probabilities. Some solution techniques are related for searching the optimal robust control policy. Finally, a numerical example is presented and analyzed.
The paper is concerned with the robust control problems for exponential controlled closed queuing networks (CCQNs) under uncertain routing probabilities. As the rows of some parameter matrices such as infinitesimal generators may be dependent, we first transform the objective vector under discounted-cost criteria into a weighed-average cost. Through the solution to Poisson equation, i.e., Markov performance potentials, we then unify both discounted-cost and average-cost problems to study, and derive the gradient formula of the new objective function with respect to the routing probabilities. Some solution techniques are related for searching the optimal robust control policy. Finally, a numerical example is presented and analyzed.
2005, 31(3): 451-458.
摘要:
Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.
Since the state of hybrid systems is determined by interacting continuous and discrete dynamics, the state estimation of hybrid systems becomes a challenging problem. It is more complicated when the discrete mode transition information is not available, and the modes of hybrid systems are nonlinear stochastic dynamic systems. To address this problem, this paper proposes a novel hybrid strong tracking filter (HSTF) for state estimation of a class of hybrid nonlinear stochastic systems with unknown mode transition, the method for designing HSTF is presented. The HSTF can estimate the continuous state and discrete mode accurately with unknown mode transition information, and the estimation of hybrid states is robust against the initial state. Simulation results illustrate the effectiveness of the proposed approach.
2005, 31(3): 459-463.
摘要:
A novel supervised receding horizon optimal scheme is presented for discrete time systems in the process control. In the employing level, PID controller is used, while the receding horizon approach is applied to the optimized level. The considered problem is to optimize the employing level PID controller parameters through minimizing a generalized predictive control criterion. Compared with a fixed parameters PID controller, the proposed algorithm provides well performance over a range of operating condition.
A novel supervised receding horizon optimal scheme is presented for discrete time systems in the process control. In the employing level, PID controller is used, while the receding horizon approach is applied to the optimized level. The considered problem is to optimize the employing level PID controller parameters through minimizing a generalized predictive control criterion. Compared with a fixed parameters PID controller, the proposed algorithm provides well performance over a range of operating condition.
2005, 31(3): 464-469.
摘要:
Monocular visual positioning for indoor mobile robot is concerned in this paper. A new visual positioning method based on homography matrix in Euclidean space is proposed. It can calculate the position and pose of the mobile robot according to the intrinsic parameters of camera and two position-known points in a plane. It is very simple and low cost in computation. The experimental results show its effectiveness.
Monocular visual positioning for indoor mobile robot is concerned in this paper. A new visual positioning method based on homography matrix in Euclidean space is proposed. It can calculate the position and pose of the mobile robot according to the intrinsic parameters of camera and two position-known points in a plane. It is very simple and low cost in computation. The experimental results show its effectiveness.
2005, 31(3): 470-474.
摘要:
Most existing algorithms for identifying multi-model system are based on minimizing the square of bias between global outputs of the actual system and the identified model, but the resultant model lacks of robustness. In order to solve this problem, this paper considers some other algorithms in which local models are identified independently and presents a multi-model identification algorithm based on weighted cost function, which uses the idea of local weighted regression and local approximation while keeps the model structure of global identification algorithm. The result of application to a 300MW unit boiler superheater illustrates that the multi-model generated by the proposed algorithm has better trade-off between global fitting and local interpretation.
Most existing algorithms for identifying multi-model system are based on minimizing the square of bias between global outputs of the actual system and the identified model, but the resultant model lacks of robustness. In order to solve this problem, this paper considers some other algorithms in which local models are identified independently and presents a multi-model identification algorithm based on weighted cost function, which uses the idea of local weighted regression and local approximation while keeps the model structure of global identification algorithm. The result of application to a 300MW unit boiler superheater illustrates that the multi-model generated by the proposed algorithm has better trade-off between global fitting and local interpretation.
2005, 31(3): 475-478.
摘要:
Some delay-dependent absolute stability criteria for Lurie control systems with time-varying delay are derived, in which some free-weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. These criteria are based on linear matrix inequality(LMI) such that the upper bound of time-delay guaranteeing the absolute stability and the free-weighting matrices can be obtained through the solutions of the LMI. Moreover, the Lyapunov functional constructed by the solutions of these LMIs is adopted to guarantee the absolute stability of the systems. Finally, some examples are provided to demonstrate the effectiveness of the proposed methods.
Some delay-dependent absolute stability criteria for Lurie control systems with time-varying delay are derived, in which some free-weighting matrices are used to express the relationships between the terms in the Leibniz-Newton formula. These criteria are based on linear matrix inequality(LMI) such that the upper bound of time-delay guaranteeing the absolute stability and the free-weighting matrices can be obtained through the solutions of the LMI. Moreover, the Lyapunov functional constructed by the solutions of these LMIs is adopted to guarantee the absolute stability of the systems. Finally, some examples are provided to demonstrate the effectiveness of the proposed methods.
2005, 31(3): 479-483.
摘要:
This paper investigates the design of robust guaranteed cost observer for a class of linear descriptor time-delay systems with jumping parameters. The system under study involves time delays, jumping parameters and uncertainties. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless observers such that for all uncertainties, the resulting augmented system is regular, impulse free, robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost observers is derived. Robust guaranteed cost observers are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.
This paper investigates the design of robust guaranteed cost observer for a class of linear descriptor time-delay systems with jumping parameters. The system under study involves time delays, jumping parameters and uncertainties. The transition of the jumping parameters in systems is governed by a finite-state Markov process. The objective is to design linear memoryless observers such that for all uncertainties, the resulting augmented system is regular, impulse free, robust stochastically stable independent of delays and satisfies the proposed guaranteed cost performance. Based on stability theory in stochastic differential equations, a sufficient condition on the existence of robust guaranteed cost observers is derived. Robust guaranteed cost observers are designed in terms of linear matrix inequalities. A convex optimization problem with LMI constraints is formulated to design the suboptimal guaranteed cost filters.
2005, 31(3): 484-490.
摘要:
A leak detection plays a key role in the overall integrity monitoring for a oil pipeline system. A fuzzy decision-making approach to pipeline leak localization is proposed in this paper. The two main methods, pressure gradient localization and negative pressure wave localization, are combined with fuzzy logical decision-making method to form a novel fault diagnosis scheme. The combination scheme can improve the precision of localization. An application example, 14km long oil pipeline leak detection and localization, is illustrated. This method is compared with others through practical experiments and its validity is confirmed by the results.
A leak detection plays a key role in the overall integrity monitoring for a oil pipeline system. A fuzzy decision-making approach to pipeline leak localization is proposed in this paper. The two main methods, pressure gradient localization and negative pressure wave localization, are combined with fuzzy logical decision-making method to form a novel fault diagnosis scheme. The combination scheme can improve the precision of localization. An application example, 14km long oil pipeline leak detection and localization, is illustrated. This method is compared with others through practical experiments and its validity is confirmed by the results.
2005, 31(3): 491-494.
摘要:
The lifting technique is now a well recognized tool for H1 design and analysis of sampled-data systems. However, the efficiency of the method depends on the structure of the problem. The structure of the H1 sensitivity problem is analyzed in this paper. And the constraints on the H1-optimization problem and on the design parameters in lifting design are also discussed. Under such constraints the resulting performance from the design is generally low. Therefore, the lifting technique can not be recommended as a synthesis tool for the sampled-data systems. An example is also given in the paper.
The lifting technique is now a well recognized tool for H1 design and analysis of sampled-data systems. However, the efficiency of the method depends on the structure of the problem. The structure of the H1 sensitivity problem is analyzed in this paper. And the constraints on the H1-optimization problem and on the design parameters in lifting design are also discussed. Under such constraints the resulting performance from the design is generally low. Therefore, the lifting technique can not be recommended as a synthesis tool for the sampled-data systems. An example is also given in the paper.
