The Robust H_∞ Control For Switched Interval Systems

Interval system is a class of important systems with parameter uncertainties.In many practical control systems,the systems' parameters may vary in a fixed interval due to the change of environment and the aging of components and parts,so it is of great theoretical and practical significance to study the robust control of interval systems.The switched system is a class of important hybrid dynamical systems, consisting of a family of subsystems and a switching rule that prescribes which subsystem is active at each time instant.The switched interval system is a class of systems which contain both switching and interval matrices,thus its dynamical performance is more complex than the general switched system.By using Lyapunov stability theory and linear matrix inequalities method,this dissertation studies the robust H_∞control for the continuous-time interval systems, the continuous-time switched interval systems and the discrete-time switched interval systems respectively with the following summarization of the full text:Firstly,the robust H_∞control for the continuous-time interval systems is studied. The robust stability as well as the disturbance attenuation level of the system is discussed based on an equivalent transformation of the interval matrices and LMI approach.The new sufficient condition for testing the robust stability and the disturbance attenuation level of the system is obtained.Then the sufficient condition is extended to robust H_∞state feedback control of the continuous-time interval system and the new sufficient condition for testing the robust stabilization along with the disturbance attenuation level of the system is obtained.Some numerical examples are given to show that the new condition gained in this dissertation is less conservative than the existing ones.Secondly,the robust H_∞control for the continuous-time switched interval system is studied.The new sufficient condition for testing the robust stability and the disturbance attenuation level of the autonomous continuous-time switched interval system is obtained by using the multiple Lyapunov functions method and Finsler's Lemma.Then two sufficient conditions for testing the robust stabilization and the disturbance attenuation level of the system are obtained according to two equivalent transformations of the interval matrix.At the end of this part,two numerical examples are given to examine and verify the correctness and effectiveness of the results,and to compare the conservativeness of the two equivalent transformations of the interval matrix.Finally,the robust H_∞control for the discrete-time switched interval system is discussed.By using multiple Lyapunov functions method and Finsler's Lemma,the new condition for determining the robust stability and the disturbance attenuation level of the discrete-time switched interval system is obtained from studying the autonomous discrete-time switched interval system.Then the new sufficient condition is extended to the state feedback control case,both the robust H_∞switched controllers and the switching rule are gained.The detailed simulation shows that the results obtained in the text are correct.This dissertation provides a new way of analyzing and synthesizing the switched system by combining Lyapunov stability theory with Finsler's Lemma.