LMI-Based Pole Assignment For Uncertain Switched Systems

Uncertain switched systems are an important class of hybrid systems. The uncertain systems mainly include two types: dynamic uncertainty and parameter uncertainty. The model's uncertainty is the combination of dynamic uncertainty and parameter uncertainty in general, and possible appear on different location of control loop. The problem of state feedback control of continuous-time switched linear systems with uncertain items is addressed in this paper. Uncertain switched systems' pole assignment and disturbance attenuation level are studied. The switched systems not only have unknown time-varying, norm-bounded uncertainty in system's structure, but also have exogenous disturbance. The details are as following:First, switched systems' pole assignment with structural uncertainty and disturbance attenuation level are studied. The switched systems not only have unknown, norm-bounded uncertainty in system structure, but also have exogenous disturbance. By using common Lyapunov function method, the state feedback robust controllers under arbitrary switching strategy are designed to assure each subsystem's eigenvalue inside a chosen circle on the open left-half complex plane and the states of the systems asymptotically stable. Then the minimum disturbance attenuation level on Lyapunov function for switched systems is obtained. All of these based on convex combinations technique and linear matrix inequalities method, the result is expressed in the form of linear matrix inequalities, which can be solved easily. The simulation shows that the conclusion is correct and effective.Second, the switched systems' pole assignment with input uncertainty and disturbance attenuation level are studied. The switched systems not only have also unknown, norm-bounded uncertainty in system's structure, but also have exogenous disturbance. By using common Lyapunov function method, the sufficient condition to make the switched system stable is expressed in the form of linear matrix inequalities. The condition assures each subsystem's eigenvalue inside a chosen circle on the open left-half complex plane. The simulation shows that the designed controller can make the states of the switched systems asymptotically stable under the arbitrary switching strategy with poles inside chosen circles and minimum disturbance attenuation level.Last, the question of the guaranteed cost of uncertain switched systems is addressed. To make the uncertain switched systems satisfy some dynamic character and static character, at the same time fulfill the request of guaranteed cost. By using the character of disc, connect the request of disc's pole constraints and guaranteed cost. The approach of the problem is addressed.Summary of the full text and the direction of next research are given at the end of this thesis.