Research On Overall Satisfaction Control For Complex Switched Linear Systems

Switched systems are the important model of hybrid systems, which are from the point of view of system and control theory. They are composed of multi subsystems ,these subsystems are not irrelevance, they are interaction, it exist a switching rule, which decide when to run the subsystem. Because of its simple structure, easy understanding,analysis and application, Switch systems have been a hot spot of the field of hybrid systems. Regardless of theory, the practice has a good development prospects.Linear Switched System is a sort of switched system, whose system function and switching control function is composed of state,switching sequence,control input and time. We often come across time-delays and something uncertain in practice, so it is necessary to research the Linear switched system.According to linear system and optimal control, the paper investigate the stability of the system, robustness and optimal control, by using linear matrix inequality as a important tool, concretely, the main research of the paper is as follows: Based on Lyapunov stability theory of hybrid systems and using linear matrix inequalities method, this dissertation mainly investigates the stability analysis and optimization control. The main contributions of this dissertation are as follows:1. First, the paper studied a convex combination condition of a sort of linear switched system with time-delays. It's composed of two parts, the first part studied a convex combination condition of a sort of linear switched system with continuation time-delays, in the second part , it studied a convex combination condition of a sort of linear switched system with discrete time-delays. It gave the convex combination condition by LMI.2. It studied the feedback stabilization of a sort of linear switched system with time-delays. According to equality constraint, the BMI can be converted into LMI, according to state transformation, the system can be converted into the system without time-delays, then, it can be researched by relevance theory of linear switched system.3. It studied state feedback of H infinity index of the system, which had discrete time-delays, It gave a convex combination condition of the system by the action of any switching signal, when the system had the performanceγof H infinity index, the form of the convex combination condition is given by LMI. On that basis, it gave the design method of the system, when it had he performanceγof H infinity index.4. The problem of state feedback with circular pole index, H∞and steady variance was studied for a class of uncertain discrete-time switched linear systems. Firstly, a sufficient condition for the closed-loop switched systems with the above indices was obtained. Next, by linear matrix inequalities approach, the design of state feedback controllers with the above three specifications was transformed into the feasible problem of some certain LMI system. The state feedback controllers can be efficiently solved by means of Matlab LMI toolbox.