Observer Design For Nonlinear Switched Systems

A switched system is a kind of very important hybrid systems. Because its model is simple and easily researched, it causes many scholars' attention and provides important theoretical value for the study of hybrid systems. The problem for the study of switched systems is mainly related to stability and the controller design, many results have been given. The observer design for switched systems is also an important aspect. This paper will consider observer design for nonlinear switched systems with Riccati inequality, and obtain sufficient conditions for extended systems of asymptotical stable using common Lyapunov function method and Lyapunov stability. When the system state can't be completely measured, the problem of observer-based robust stabilization is studied.Some results obtained are improved and perfected. This paper is divided into four parts:The first part: The concept and developed situation for switched systems are summarized, observer and robust control are briefly introduced.The second part: The problem of observer design for a class of uncertain nonlinear switched systems and a class of uncertain time-delay nonlinear switched systems is researched. This paper gives sufficient conditions for extended systems of asymptotical stable with the use of the method of common Lyapunov function and Lyapunov stability, then gets asymptotically stable observer. For a class of uncertain nonlinear switched systems, the correctness of conclusion is proved through example.The third part: The problem of robust stabilization for a class of uncertain nonlinear switched systems and a class of uncertain time-delay nonlinear switched systems is researched. The condition of observer-based robust stabilization is obtained with the use of the method of common Lyapunov function and Lyapunov stability.The fourth part: At last summary is done for the whole paper, and future work is prospected.