Delay Dependent Stability Analysis And State Feedback Control Of Time Varying Delay Systems

Time-delay systems has attracted an increasing attention of research of control theory.Time-delay widely exists in various actual systems,and seriously affects the dynamic performance of the actual systems.If we ignore the influence of time-delay when the systems is modeled,it will reduce the performance of the systems and even make the systems instability,so the research on time-delay systems has important theoretical value and practical significance.However,it is difficult to find a unified theory to solve such problem,so we ought to make a concrete analysis according to the structural characteristics of the systems.Based on some existing studies,this dissertation makes a deep analysis on the linear interval systems with time-varying delays and nonlinear Luire systems with time-varying delays.Constructing the Lyapunov functional with more information and reducing the degree of magnification can effectively optimize the results.When considering the linear interval systems with time-varying delays,more delay information is included as far as possible in constructing the Lyapunov functional.The Jensen inequality combined with reciprocal convex combination method and the Jensen inequality combined with the free weighting matrix method are used to define the integral term of the functional derivative,and the delay-dependent stability criterion is proposed.When considering the nonlinear Lurie systems with time-varying delays,more systems information is included as far as possible in constructing the Lyapunov functional.The Wirtinger inequality combined with the reciprocal convex combination method are used to define the integral term of the functional derivative and the S-procedure is used to deal with the functional derivative,and the delay-dependent stability criterion is proposed.The Lyapunov functional which makes the systems asymptotic stable is presented by solving the linear matrix inequality through MATLAB.Based on the stability criterion of the systems,the sufficient conditions for H_? performance of the systems are given,and the state feedback controller of the systems is designed.The state feedback gain matrix of the systems is obtained by MATLAB simulation and the Simulink model is built.Finally,numerical examples are provided to illustrate the effectiveness of the developed methods.