Analysis And Control Synthesis Of Switched Systems

Hybrid dynamic systems are a class of systems which contain both discrete event dynamic systems and continuous or discrete time dynamic systems, and among them there exists interaction. Switched systems are an important class of hybrid dynamic systems, which are composed of a family of subsystems and a rule orchestrating the switching between the subsystems. Switched systems are widely used in many practical problems, such as robotic systems, web switching of electric systems and sampled-data control systems, et, al. The nature of switched systems is switching, however it is not the simple addition of those of different subsystems and has some particularity and complexity. Therefore, the investigation of switched systems is very necessary. The analysis and control synthesis of switched systems are discussed in this paper. The contents of this paper are the followings:Firstly, the engineering background, characteristics, research content, and the recent development of hybrid systems and switched systems are briefly introduced.Secondly, the structure of switched systems is firstly introduced. And then the recent developments in stability analysis and feedback control of switched systems are reviewed.Thirdly, controllability and observability of switched systems are investigated. Firstly, the recent developments in controllability and observability for switched system are reviewed. Secondly, by means of properties of invariant subspace, the controllability for switched systems with continuous-time and discrete-time subsystems, and a class of discrete impulsive switched systems is respectively investigated. Some sufficient and necessary conditions of controllability are proved. In the end, some simple criterions for controllability and observability of switched symmetric composite systems are set up.Fourthly, we study the problem of robust guaranteed cost control for a class of uncertain linear discrete-time switched systems by employing average dwell time method. The design of state feedback controllers are derived in terms of LMIs such that the resulting closed-loop system is asymptotically stable for all admissible uncertainties and has a weighted guaranteed cost upper bound. A numerical example demonstrates the validity of the proposed design approach.At last, it contains a conclusion with discussions on some problems and directions for future study.