CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (9): 1051-1062.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE

谢广明, 王龙, 叶庆凯

Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China

收稿日期:2002-01-29 修回日期:2003-05-28 出版日期:2003-09-18 发布日期:2003-09-18
基金资助:
the National Natural Science Foundation of China (69925307, 60274001);the National Key Basic Research and Development Program (2002CB312200);the Postdoctoral Program Foundation of China

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE

XIE Guang-ming, WANG Long, YE Qing-kai

Department of Mechanics and Engineering Science, Peking University, Beijing 100871, P. R. China

Received:2002-01-29 Revised:2003-05-28 Online:2003-09-18 Published:2003-09-18
Supported by:
the National Natural Science Foundation of China (69925307, 60274001);the National Key Basic Research and Development Program (2002CB312200);the Postdoctoral Program Foundation of China

摘要/Abstract

摘要： The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the second part. The definition and determination of controllability of switched linear systems with single time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the one-periodic, multiple-periodic controllability of periodic-type systems and controllability of periodic systems are presented, respectively.

中图分类号:

谢广明;王龙;叶庆凯. CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 1051-1062.

XIE Guang-ming;WANG Long;YE Qing-kai . CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 1051-1062.

参考文献

[1] Liberzon A S, Morse A S. Basic problems in stability and design of switched systems [J]. IEEE Contr Syst Mag, 1999, 19(5):59-70.
[2] Ezzine J. Haddad A H. Controllability and observability of hybrid system[J]. Int J Control, 1989, 49(6):2045-2055.
[3] SUN Zhen-dong, ZHENG Da-zhong. On reachability and stabilization of switched linear systems[J]. IEEE Trans Automat Contr, 2001, 46 (2):291-295.
[4] XIE Guang-ming, ZHENG Da-zhong. On the controllability and reachability of a class of hybrid dynamical systems[A]. In:QIN Hua-shu Ed. Proceedings of the 19 th Chinese Control Conference[C]. Hong Kong:Hong Kong Engineering Counci, 2000, 114-117. (in Chinese).
[5] XIE Guang-ming, WANG Long. Necessary and sufficient conditions for controllability of switched linear systems [A]. In:American Automatic Control Counci Ed. Proceedings of the American Control Conference 2002 [C]. USA:IEEE Service Center, 2002, 1897-1902.
[6] XU Xu-ping, Antsaklis P J. On the reachability of a class of second-order switched systems [A].In:American Automatic Control Counci Ed. Proceedings of the American Control Conference 1999[C]. USA:IEEE Service Center, 1999, 2955-2959.
[7] Ishii H, Francis B A. Stabilization with control networks [J]. Automatica, 2002, 38 (10):1745 -1751.
[8] Ishii H, Francis B A. Stabilizing a linear system by switching control with dwell time[A]. In:American Automatic Control Counci Ed. Proceedings of the American Control Conference 2001[C]. USA:IEEE Service Center, 2001, 1876-1881.
[9] Morse A S. Supervisory control of families of linear set-point controllers-Part 1:Exact matching[J]. IEEE Trans Automat Contr, 1996, 41(7):1413-1431.
[10] Liberzon D, Hespanha J P, Morse A S. Stability of switched systems:a Lie-algebraic condition[J].Systems and Control Letters, 1999, 37 (3):117-122.
[11] Hespanha J P, Morse A S. Stability of switched systems with average dwell-time [A]. In:IEEE Control Systems Society Ed. Proceedings of the 38 th Conference on Decesion and Control [C].USA:IEEE Customer Service, 1999, 2655-2660.
[12] Narendra K S, Balakrishnan J. A common Lyapunov function for stable LTl systems with commuting A- matrices [J]. IEEE Trans Automat Contr, 1994, 39 (12):2469-2471.
[13] Narendra K S, Balakrishnan J. Adaptive control using multiple models[J]. IEEE Trans Automat Contr, 1997, 42(1):171-187.
[14] Petterson S, Lennartson B. Stability and robustness for hybrid systems [A]. In:IEEE Control Systems Society Ed. Proceedings of the 35th Conference on Decesion and Control[C]. USA:IEEE Customer Service, 1996, 1202-1207.
[15] YE Hong, Michel A N, HOU Ling. Stability theory for hybrid dynamical systems[J]. IEEE Trans Automat Contr, 1998, 43(4):461-474.
[16] HU Bo, XU Xu-ping, Antsaklis P J, et al. Robust stabilizing control laws for a class of second-order switched systems[J]. Systems and Control Letters, 1999, 38(2):197-207.
[17] Branicky M S. Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE Trans Automat Contr, 1998, 43(4):475-482.
[18] Shorten R N, Narendra K S. On the stability and existence of common Lyapunov functions for stable linear switching systems [A]. In:IEEE Control Systems Society Ed. Proceedings of the 37th Conference on Decesion and Control [C]. USA:IEEE Customer Service, 1998, 3723-3724.
[19] Johansson M, Rantzer A. Computation of piecewise quadratic Lyapunov funtions for hybrid systems[J]. IEEE Trans Automat Contr, 1998, 43(4):555-559.
[20] Wicks M A, Peleties P, DeCarlo R A. Construction of piecewise Lyapunov funtions for stabilizing switched systems[A]. In:IEEE Control Systems Society Ed. Proceedings of the 33 th Conference on Decesion and Control[C]. USA:IEEE Customer Service, 1994, 3492-3497.
[21] Peleties P, DeCarlo R A. Asymptotic stability of m- switched systems using Lyapunov-like functions[A]. In:American Automatic Control Counci Ed. Proceedings of the American Control Conference 1991 [C]. USA:IEEE Service Center, 1991, 1679-1684.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME-DELAY CASE

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