Controllability of a Class of Hybrid Dynamic Systems(Ⅲ)—Multiple Time-Delay Case

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

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(9): 940-950

XIE Guang-ming, WANG Long, YE Qing-kai. Controllability of a Class of Hybrid Dynamic Systems(Ⅲ)—Multiple Time-Delay Case[J]. Applied Mathematics and Mechanics, 2003, 24(9): 940-950.

Citation:

XIE Guang-ming, WANG Long, YE Qing-kai. Controllability of a Class of Hybrid Dynamic Systems(Ⅲ)—Multiple Time-Delay Case[J]. Applied Mathematics and Mechanics, 2003, 24(9): 940-950.

Citation:

XIE Guang-ming, WANG Long, YE Qing-kai. Controllability of a Class of Hybrid Dynamic Systems(Ⅲ)—Multiple Time-Delay Case[J]. Applied Mathematics and Mechanics, 2003, 24(9): 940-950.

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Controllability of a Class of Hybrid Dynamic Systems(Ⅲ)—Multiple Time-Delay Case

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

Received Date: 2002-01-29
Rev Recd Date: 2003-05-28
Publish Date: 2003-09-15

Abstract

Abstract

The controllability for switched linear systems with time-delay in controls is first investigated. The whole work contains three parts. This is the third part. The definition and determination of controllability of switched linear systems with multiple time-delay in control functions is mainly investigated. The sufficient and necessary conditions for the 1-periodic, multiple-periodic controllability of periodic-type systems and controllability of aperiodic systems are presented, respectively. Finally, the case of distinct delays is discussed, it is shown that the controllability is independent of the size of delays.
- hybrid dynamic system,
- switched linear system,
- time-delay,
- controllability,
- controllable set,
- switching sequence,
- swit ching path

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References(21)

References

[1]	Liberzon A S,Morse A S.Basic problms 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]	谢广明,郑大钟.On the controllability and reachability of a class of hybrid dynamical systems[A].见:秦化淑编.19届中国控制会议[C].香港:香港工程师协会,2000,114-117.
[5]	XIE Guang-ming,WANG Long.Necessary and sufficient conditions or 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-Part1: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 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,Peleties P,DeCarlo R A.Construction of piecewise Lyapunov funtions for stabilizing switched systems[A].In:IEEE Control Systems Society Ed.Proceedings of the 33th 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 American Control Conference 1991[C].USA:IEEE Service Centet,1991,1679-1684.