Study Of Robust Control And Filtering Approach For Nonlinear Switched Systems

With the development of science and technology, control systems become more and more complicated. It is inevitable that actuator failures or sensor failures may exist in the systems, which will affect the stability and other performance of the systems. Therefore, the demands for reliability, safety and efficiency of systems are higher and higher. Nonlinear switched systems are special and important kinds of hybrid systems, whose mathematical models can represent a class of actual engineering processes objectively. Because of the interaction between the continuous dynamics of nonlinear switched systems and the discrete switched rules, the dynamic behavior of nonlinear switched systems becomes very complicated. Many important problems have not been investigated further on these topics so far.Therefore, the studies of the reliable control and filtering for nonlinear switched systems have very important theoretical and practical significance. And they are also hotspot problems in the researches of current control field. This dissertation deals with the problems of robust stability analysis, reliable control and reliable filtering for a class of switched systems with nonlinear functions satisfying Lipschitz conditions. The main contributions are as follows:Firstly, based on Lyapunov stability theory and average dwell time (ADT) approach, the exponential stability analysis is studied for a class of nonlinear switched systems with uncertainties and time-varying delays. On the basis of it, the H∞ performance index and the L2-L∞ performance index are analyzed. Choose the continuous gain actuator failure models, which is more practical than the discrete actuator failure model, to describe the actuator failure parts. Then, robust H∞ reliable control problems and robust L2-L∞ reliable control problems are discussed bu using H∞ and L2-L∞ control methods.Secondly, the exponential stability analysis and design problems of robust L2-L∞ and H∞ reliable controllers are studied for a class of discrete time-delay nonlinear switched systems with uncertainties. The sufficient conditions are first proposed to guarantee the global exponential stability with guaranteed H∞ and L2-L∞ performances for the discrete nonlinear switched systems by using piecewise Lyapunov functional and ADT approach. Then, the corresponding solvability conditions for the desired robust H∞ and L2-L∞ reliable controllers are established, and they are cast into convex optimization problems.Finally, robust filtering problems are investigated for a class of continuous nonlinear switched systems with sensor failures. Based on Lyapunov stability theory and average dwell time approach, the sufficient conditions are proposed to guarantee the global exponential stability with guaranteed H∞ and L2-L∞ performances for the continuous nonlinear switched systems with sensor failures. Select the continuous gain actuator failure models, so that the sensor failures are more grounded in reality. Then, inequalities can be solved by using variable substitution method. At last, simulation results are provided to demonstrate that the proposed designed schemes can meet the filtering requirements.