CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (9): 1041-1050.

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

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:2003-03-25 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 Reasearch and Development Program (2002CB312200);the Postdoctoral Program Foundation of China

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

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:2003-03-25 Online:2003-09-18 Published:2003-09-18
Supported by:
the National Natural Science Foundation of China (69925307, 60274001);the National Key Basic Reasearch and Development Program (2002CB312200);the Postdoctoral Program Foundation of China

摘要/Abstract

摘要： The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.

Abstract: The controllability for switched linear system with time-delay in controls was first investigated. The whole work contains three parts. This is the first part, including problem formulation and some preliminaries. Firstly, the mathematical model of switched linear systems with time-delay in control functions was presented. Secondly, the concept of column space, cyclic invariant subspace and generalized cyclic invariant subspace were introduced. And some basic properties, such as separation lemma, were presented. Finally, a basic lemma was given to reveal the relation between the solution set of a centain integral equations and the generalized cyclic invariant subspace. This lemma will play an important role in the determination of controllability. All these definitions and lemmas are necessary research tools for controllability analysis.

中图分类号:

谢广明;王龙;叶庆凯. CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 1041-1050.

XIE Guang-ming;WANG Long;YE Qing-kai . CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(9): 1041-1050.

参考文献

[1] Liberzon A B, 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 systems[J]. Int J Control, 1989, 49(6):2045-2055.
[3] SUN Zheng-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 dynmaical systems[A]. In QIN Hua-shu Ed. Proceedings of the 19th Chinese Control Conference[C]. Hong Kong:Hong Kong Engineering Counci, 2000, 114-117. (in Chinese).
[5] XIE Guang-ning, WANG Long. Necessary and sufficient conditions for controllability of switched linear systems[A]. In:American Automatic Control Counci Ed. Proceedings of the American Contron 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 Contr Lett, 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 38th 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 LTI 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, Pelefies 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 Antomafic Control Counci Ed. Proceedings of the American Control Conference 1991[C]. USA:IEEE Service Center, 1991, 1679-1684.
[22] Chyung D H. Oh the controllability of linear systems with delay in control[J]. IEEE Trans Automat Contr, 1970, 15(2):694-695.
[23] Chyung D H. Controllability of linear systems with multiple delays in control[J]. IEEE Trans Automat Contr, 1970, 15 (6):694-695.
[24] HUANG Lin. Linear Algebra in Systems and Control Theory [M]. Beijing:Science Press, 1984.(in Chinese)

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅰ)—BASIC PROPERTIES AND PRELIMINARY RESULTS

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