Journal of South China University of Technology (Natural Science Edition) ›› 2008, Vol. 36 ›› Issue (9): 140-144.

• Electronics, Communication & Automation Technology • Previous Articles    

LMI Solution to Invariant Set in a Class of Hybrid System

Li Jian-qiang  Pei Hai-long  Yuan Ling   

  1. School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, Guangdong, China
  • Received:2007-09-05 Revised:2008-03-08 Online:2008-09-25 Published:2008-09-25
  • Contact: 李坚强（1980-），男，博士，主要从事混合系统、嵌入式系统研究． E-mail:aujqli@163．com
  • About author:李坚强（1980-），男，博士，主要从事混合系统、嵌入式系统研究．
  • Supported by:

    国家自然科学基金资助项目（60374036,60574004,60736024）;高校博十点基金资助项目（20040561031）;广东省自然科学基金资助项目（20040561031）

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Abstract:

In order to solve the problem of existence of the invariant sets in hybrid systems, a class of hybrid system with perturbed disturbance is investigated. By proposing a common Lyapunov function, the existence of invariant set is proved. Moreover, by constructing a Lyapunov function, the existence is calculated based on the linear matrix inequality （LMI） method, the switch laws and sub-system domains of the hybrid system are obtained, and the do- main of the invariant set is further computed. A numerical example is finally presented to confirm the feasibility and effectiveness of the proposed method.

Key words: hybrid system, invariant set, Lyapunov function, linear matrix inequality