The Stability Analysis And Synthesis For Saturation Nonlinear Systems With Time-delay

In the practical engineering problems, the saturation is a common nonlinear phenomenon. The characteristic of saturation nonlinearity is nonsmooth, so the dynamic performance of the system will be seriously affected and the system will be unstable. Therefore, the research for saturation system is quite necessary. In recent years, saturation systems have caused the wide attention of scholars both at home and abroad.Stability is a prerequisite for normal operation of system. So it is mainly studied in this thesis. This thesis studies the uncertain time-delay state saturation system, uncertain discrete time-delay system with part state saturation and time-varying delay control system with actuator saturation. Main methods of the research are included as follow: applying the Lyapunov stability theorem, applying convex combination method or fan-shaped area method to deal with the saturation. Then the necessary and sufficient condition of the stability of the system is given and the state feedback controller is designed.The concrete contents of the thesis are summarized as follows:Firstly, the thesis gives a brief presentation about the research background and significance of saturation system as well as the research status of saturation system. At the same time it provides the simple saturation system model, the three ways of dealing with saturation. The related concepts such as stability and the knowledge of the linear matrix inequalities (LMIs) are introduced.Secondly, the thesis focuses on the stability problems of the uncertain state saturation system with time-delay. With the help of a convex combination method and Lyapunov stability theory, the sufficient conditions for the wide range asymptotic stability of systems is gained. Through the variable transformation and matrix theory, the sufficient conditions for the stability of system are converted to linear matrix inequality form. At the same time the state feedback controller of the system is designed.Thirdly, we expound the stability of a class of uncertain discrete time-delay system with part state saturation. By introducing a special matrix, saturated part is processed. The uncertainty parameter matrix is processed by the method of handling uncertainty parameter matrix at the same time. Applying discrete Lyapunov stability theorem, the global asymptotic stability criterion is presented.Fourthly, the thesis is mainly in view of the stability of the uncertain and time-varying delay system with actuator saturation. Assuming that uncertainty meets the norm bounded uncertainty conditions, actuator saturation part is dealt by the method of nonlinear fan area and time-delay is dealt by interactive convex combination method. Applying Lyapunov-Krasovskii functional method, the delay-dependent stability criterion and the design method of state feedback controller are gained.Finally, we summarize the full text and point out future research work.