Stability Analysis And L₂-Gain Control For Several Nonlinear Switching Singular Systems

Singular system is a class of more practical system,the analysis and design methods of singular system have attracted much attention in theory and application.Switching system,as a class of hybrid system requires higher stability than normal systems.In the switching process and practical work,switching system often produces pulse behavior,and its switching rules play a crucial role.In practice,complete linear systems do not exist.Therefore,this thesis studies the stability problems of several nonlinear switching singular systems,which gradually increases the complexity of the system and makes the research results practically more significance.The main research work in this thesis is as follows:1.The stability and L2-gain performance for a class of switching singular system with time varying delay are studied.Firstly,the system stability is analyzed and sufficient conditions for the L2-gain performance are given;Secondly,using the linear matrix inequalities and the model dependent average dwell time method,an effective design method of the state feedback controller with L2-gain performance is proposed;Finally,give numerical examples.2.For a class of nonlinear switching singular systems with pulse,the stability and L2gain performance were studied.Firstly,the system stability is analyzed and provide sufficient conditions for system exponential stability and L2-gain performance;Secondly,a state feedback controller is designed to make sure the system stable and have L2-gain performance;Finally,give numerical examples.3.A state observer design method is proposed for a class of nonlinear switched singular systems with time-varying delays.Firstly,analyze the system stability based on Lyapunov stability theory and provide sufficient conditions for time-delay system stability and L2-gain performance;Secondly,design the controller stabilizes the closed loop system and provide numerical examples.Finally,design a state feedback controller based on the observer to solve the problem.4.The design method of a state observer is proposed for a class of uncertain nonlinear switching singular systems with time varying delay.Firstly,sufficient conditions for robust stability and weighted L2-gain performance are given.Secondly,an effective design method of state feedback controller with L2-gain performance is proposed with numerical examples.Finally,observer based on state feedback controller is designed.