H₂/H_∞ Control Of Switched Systems Based On LMI

Hybrid systems are a class of systems which contain both discrete event dynamic and continuous-time or discrete-time dynamic systems, and among them there exists interaction. Switched systems are an important kind of hybrid systems, which are composed of a family of subsystems and a switching law. Because switched systems have special properties, the research is more difficult. The stability of a switched system not only depends on its subsystems, but also relies upon the switching strategy. Switched systems are in many practical applications, such as robotic systems, electric power grids and sampled-data control systems. Therefore, the research on stability and robustness of of switched systems is very important and necessary.In this dissertation, H 2 control, H₂/H_∞control and robust control for a class of linear switched systems are investigated, respectively, which is involved as follows.Firstly, a sufficient condition for the existence of controllers and switching law for a class of linear switched systems is proposed, which enables the closed-loop switched systems asymptotically stable and satisfies the H 2 performance.Secondly, H₂/H_∞state feedback control for a class of continuous-time switched systems is developed based on LMI method. The convex optimization problem is established for H₂/H_∞robust control and its optimization solution is given which has smaller conservative property.Finally, H∞and H₂/H_∞robust control for a class of switched discrete-time systems with parameter uncertainty and external disturbance are presented, respectively, based on multiple Lyapunov function method. Besides, the convex optimization problem and its optimization solution is given which has smaller conservative property.