变时滞不确定Lurie系统的时滞分布依赖鲁棒稳定性分析
doi: 10.3724/SP.J.1004.2012.01100
Delay-distribution-dependent Robust Stability Analysis of Uncertain Lurie Systems with Time-varying Delay
-
Abstract: In this paper, the problem of robust absolute stability of Lurie system with probabilistic time-varying delay and norm-bounded parametric uncertainty is considered. The time delay variation range is divided into two sub-intervals. By considering the probability distribution of the time-varying delay between the two sub-intervals and the knowledge of the delay variation range, a novel linear matrix inequalities (LMIs) based stability condition is derived by defining a Lyapunov Krasovskii functional. It is illustrated with the help of numerical examples that the derived stability criteria can lead to less conservative results as compared to the results obtained by the traditional method of using the delay variation range information only.
-
[1] Popov V M. Absolute stability of nonlinear systems of automatic control. Automation and Remote Control, 1962, 22(8): 857-875[2] Park P. A revisited Popov criterion for nonlinear Lur'e systems with sector-restrictions. International Journal of Control, 1997, 68(3): 461-469[3] Liao X, Yu P. Absolute Stability of Nonlinear Control Systems (Second edition). Dordrecht: Springer, 2008[4] Bliman P A. Lyapunov-Krasovskii functionals and frequency domain: delay-independent absolute stability criteria for delay systems. International Journal of Robust and Nonlinear Control, 2001, 11(8): 771-788[5] He Y, Wu M. Absolute stability for multiple delay general Lur'e control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics, 2003, 159(2): 241-248[6] Yu L, Han Q L, Yu S, Gao J. Delay-dependent conditions for robust absolute stability of uncertain time-delay systems. In: Proceedings of the 42nd IEEE Conference on Decision and Control. Hawaii, USA: IEEE, 2003. 6033-6037[7] Han Q L. Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica, 2005, 41(12): 2171-2176[8] He Y, Wu M, She J H, Liu G P. Robust stability for delay Lur'e control systems with multiple nonlinearities. Journal of Computational and Applied Mathematics, 2005, 176(2): 371-380[9] Lee S M, Park J H. Delay-dependent criteria for absolute stability of uncertain time-delayed Lur'e dynamical systems. Journal of the Franklin Institute, 2010, 347(1): 146-153[10] Cao J, Zhong S, Hu Y. Delay-dependent condition for absolute stability of Lurie control systems with multiple time delays and nonlinearities. Journal of Mathematical Analysis and Applications, 2008, 338(1): 497-504[11] Han Q L. A new delay-dependent absolute stability criterion for a class of nonlinear neutral systems. Automatica, 2008, 44(1): 272-277[12] Liu X, Wang J, Duan Z, Huang L. New absolute stability criteria for time-delay Lur'e systems with sector-bounded nonlinearity. International Journal of Robust and Nonlinear Control, 2010, 20(6): 659-672[13] Han Q L, Yue D. Absolute stability of Lur'e systems with time-varying delay. IET Control Theory and Applications, 2007, 1(3): 854-859[14] Wu M, Feng Z Y, He Y, She J H. Improved delay-dependent absolute stability and robust stability for a class of nonlinear systems with a time varying delay. International Journal of Robust and Nonlinear Control, 2010, 20(6): 694-702[15] Gao J F, Pan H P, Ji X F. A new delay-dependent absolute stability criterion for Lurie systems with time-varying delay. Acta Automatica Sinica, 2010, 36(6): 845-850[16] Qiu F, Cui B, Ji Y. Delay-dividing approach for absolute stability of Lurie control system with mixed delays. Nonlinear Analysis: Real World Applications, 2010, 11(4): 3110-3120[17] Yue D, Tian E, Wang Z, Lam J. Stabilization of systems with probabilistic interval input delays and its applications to networked control systems. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 2009, 39(4): 939-945[18] Zeng H B, He Y, Wu M, Xiao S P. Absolute stability and stabilization for Lurie networked control systems. International Journal of Robust and Nonlinear Control, 2011, 21(14): 1667-1676[19] Mao X. Exponential stability of stochastic delay interval systems with Markovian switching. IEEE Transactions on Automatic Control, 2002, 47(10): 1604-1612[20] Xu S, Chen T. Robust H∞ control for uncertain stochastic systems with state delay. IEEE Transactions on Automatic Control, 2002, 47(12): 2089-2094[21] Boyd S, Ghaouri L E, Feron E, Balakrishnan V. Linear Matrix Inequalities in System and Control Theory. Philadelphia: SIAM, 1994[22] Petersen I R. A stabilization algorithm for a class of uncertain linear systems. Systems and Control Letters, 1987, 8(4): 351-357[23] Khalil H K. Nonlinear Systems. New Jersey: Prentice-Hall, 1996[24] Hao F, Zhao X. Absolute stability of Lurie networked control systems. International Journal of Robust and Nonlinear Control, 2010, 20(12): 1326-1337
点击查看大图
计量
- 文章访问数: 1731
- HTML全文浏览量: 15
- PDF下载量: 783
- 被引次数: 0