Study On The Stability Of Switched Linear Systems

The systems which contain analog variables and logic variables are called Hybrid Systems customarily. There is one class of hybrid systems which consist of more than one sub-system. All of these sub-systems are activated as the system's model in special conditions. The state trajectory of system is continuous at the time of the system's model changed. They are called Switched Systems usually. If all the sub-models are linear systems, it is called Switched Linear Systems. For Example, a system who has its input-out characteristic curve saturated is a switched linear system with being piece-wisely linearized.The stability of switched linear systems is a challenging problem because of its varying structure. The stability lies on not only the stability of sub-systems, but also the switching sequences. The main focus of this paper is founding the criteria of stability of switched linear systems.Two methods as the criteria of stability for switched linear systems are studied in this paper.For a class of switched linear systems, the matrix measure has been applied to the judging systems stable or unstable under arbitrary switching sequences or given switching sequence. It is also used to study the system which is unstable under arbitrary switching sequence. Simple algorithm of matrix measure has this method more attritive. Especially, it is very simple in high order systems and time varying systems.On the base of common Lyapunov function, energy function and energy velocity matrix are used to studying the criteria of stability of switched linear systems. Besides used to identify if a switched linear system is stable or not under arbitrary switching sequences, these methods can be as a director in designing stable switching sequence. This is the differential from other Lyapunov functions methods.All the two methods in this paper have the same merit that they are all easily applied in practice.Besides, The multiple Lyapunov functions and the common Lyapunov function are expatiated in detail in this paper. On the same time, controllability, observability, feedback equivalence and optimal control are contained in this paper abstractly. Hopes it can be help for the people who want to know these branches roundly.The conclusion and perspective are given at the end of the dissertation. The appendix are the MATLAB programs for all of the examples in this paper. The readers can use them to certificate the examples in this paper.