Input-output Finite-time Stability of Linear Time-varying Descriptor Impulse Systems
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摘要: 研究了广义时变脉冲系统的输入输出时域稳定问题.基于矩阵微分不等式(Differential matrix inequalities,DMI),给出了两个上述系统输入输出时域稳定的充分条件分别对应 L2干扰输入和 L∞干扰输入.这样的条件要求矩阵微分不等式解的存在性.接下来根据给出的充分条件设计了控制器,使得闭环系统输入输出时域稳定.本文的结果对于一般情况下的广义时变系统同样适用.最后,给出了两个算例来验证结果的有效性.Abstract: This paper deals with the input-output finite-time stability problem for continuous-time linear time-varying descriptor impulse systems. The output and input refer to the controlled output and the disturbance input, respectively. Two classes of disturbance inputs are considered, which belong to L2 and L∞. New results for the above-mentioned class of systems are presented in the form of sufficient conditions given in terms of differential matrix inequalities. Based on the two conditions, state feedback controllers are designed such that the resultant closed-loop systems are input-output finite-time stable. The result also apply to time-varying descriptor systems. Finally, two examples are presented to show the validity of the new results.
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[1] Amato F, Ambrosino R, Cosentino C, De Tommasi G. Input-output finite-time stabilization of linear systems. Automatica, 2010, 46(9): 1558-1562 [2] Amato F, Carannante G, De Tommasi G, Pironti A. Input-output finite-time stabilization of LTV systems via dynamic output feedback. In: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). Orlando, FL: IEEE, 2011. 1928-1932 [3] Amato F, Carannante G, De Tommasi G, Pironti A. Input-output finite-time stability of linear systems: necessary and sufficient conditions. IEEE Transactions on Automatic Control, to be published [4] Amato F, Carannante G, De Tommasi G, Pironti A. Necessary and sufficient conditions for input-output finite-time stabilization of linear time-varying systems. In: Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC). Orlando, FL: IEEE, 2011. 1933-1937 [5] Amato F, Carannante G, De Tommasi G, Pironti A. Input-output finite-time stabilization with constrained control inputs. In: Proceedings of the 51st IEEE Conference on Decision and Control. Maui, Hawaii: IEEE, 2012. 5731-5736 [6] Kamenkov G. On stability of motion over a finite interval of time. Journal of Applied Mathematics and Mechanics, 1953, 17: 529-540 [7] Lebedev A. On stability of motion during a given interval of time. Journal of Applied Mathematics and Mechanics, 1954, 18: 139-148 [8] Weiss L, Indante E. Finite-time stability under perturbing forces and on product spaces. IEEE Transactions on Automatic Control, 1967, 12(1): 54-59 [9] Amato F, Ambrosino R, Ariola M, Cosentino C. Finite-time stability of linear time-varying systems with jumps. Automatica, 2009, 45(5): 1354-1358 [10] Amato F, Ambrosino R, Cosentino C. Finite-time stability of linear time-varying systems: analysis and controller design. IEEE Transactions on Automatic Control, 2010, 55(4): 1003-1008 [11] Amato F, Ariola M, Cosentino C. Finite-time stabilization via dynamic output feedback. Automatica, 2006, 42(2): 337-342 [12] Garcia G, Tarbouriech S, Bernussou J. Finite-time stabilization of linear time-varying continuous systems. IEEE Transactions on Automatic Control, 2009, 54(2): 364-369 [13] Shen Y J. Finite-time control of linear parameter-varying systems with norm-bounded exogenous disturbance. Journal of Control Theory and Applications, 2008, 6(2): 184-188 [14] Liu L, Sun J T. Finite-time stabilization of linear systems via impulsive control. International Journal of Control, 2008, 81(6): 905-909 [15] Wang C J. Controllability and observability of linear time-varying singular systems. IEEE Transactions on Automatic Control, 1999, 44(10): 1901-1905 [16] Zhang Xue-Feng, Zhang Qing-Ling. On controllability and observability of linear time-varying singular systems. Acta Automatica Sinica, 2009, 35(9): 1249-1253(张雪峰, 张庆灵. 线性时变广义系统的能控性和能观性问题. 自动化学报, 2009, 35(9): 1249-1253) [17] Wang C J. Impulse observability and impulse controllability of linear time-varying singular systems. Automatica, 2001, 37(11): 1867-1872 [18] Kabla N A, Debeljković D L J. Finite-time stability of time-varying linear singular systems. In: Proceedings of the 37th IEEE Conference on Decision and Control. Belgrade: IEEE, 1998 [19] Kabla N A, Debeljković D L J. Finite-time stability robustness of time-varying linear singular systems. In: Proceedings of the 3rd Asian Control Conference. Shanghai: IEEE, 2000 [20] Kabla N A, Debeljković D L J. Finite-time instability of time-varying linear singular systems. In: Proceedings of the 1999 American Control Conference. San Diego: IEEE, 1999. 1796-1800 [21] Su Xiao-Ming, Lv Ming-Zhu. Analysis of robust stability for linear time-varying uncertain periodic descriptor systems. Acta Automatica Sinica, 2006, 32(4): 481-488 (苏晓明, 吕明珠. 广义不确定周期时变系统的鲁棒稳定性分析. 自动化学报, 32(4): 481-488) [22] Wang Xiao-Hua, Liu Xiao-Ping. Disturbance decoupling of nonlinear generalized time-varying systems. Acta Automatica Sinica, 2000, 26(6): 798-820 (王晓华, 刘晓平. 非线性广义时变系统的干扰解耦. 自动化学报, 2000, 26(6): 798-820) [23] Zhao S W, Sun J T, Liu L. Finite-time stability of linear time-varying singular systems with impulsive effects. International Journal of Control, 2008, 81(11): 1824-1829 [24] Xu J, Sun J. Finite-time stability of linear time-varying singular impulsive systems. IET Control Theory Applications, 2010, 4(10): 2239-2244
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