Robust Control Of Saturated Systems With Time Delays

This thesis is dedicated to the study of the robust control problems of saturated uncertain time-varying delay systems. As is known to all, delays, uncertainties, and saturated nonlinearity etc are ubiquitous in actual systems, and will always seriously affect the stability and the performance index of the control system. Delays are inherent for general systems, and the uncertainties are inevitable in actual systems. In addition, saturation is a special kind of nonlinearity. Almost all the physical links have saturation. If such nonlinear characteristics are not considered in the design of controller, integral saturated or limit cycle may occur. Therefore, the research of saturation is also very important. It can not only improve nonlinear system theory, but also greatly promote the application of saturation system theory in actual systems.At present, the treatment for saturated nonlinearity can be summarized as two ways. The first is that the saturation is not considered in the first stage of the design of control system.Then some measures are added to deal with the side-effects of saturation. This method can obviously improve the performance of the system, but fails to consider the system stability properties. The second is that the saturation is considered in the initial phase of the design of control system. This is the mainstream of the present research. This thesis mainly consider systems that contains time-varying delays, uncertainties and saturated nonlinearity at the same time, based on the Lyapunov stability theory, by means of integral inequality, matrix analysis and the linear matrix inequalities(LMI), it studies the stability problems of the system, and then make further research of controller design problem on this basis. The research content is divided into two parts:Firstly, the thesis uses the matrix decomposition method and Lyapunov-Krasovskii functional method combines the S-process to discuss the delay-dependent robust stabilization problems of the saturated uncertain linear systems that contains input delays and state delays at the same time. The derivative of V, the Lyapunov function, is dealt by Integral inequality. Based on the method of LMI, a sufficient condition for robust stabilization by memoryless state feedback is obtained. An example is presented. MATLAB is used to solve the corresponding linear matrix inequalitie. The effectiveness of the result is showed.Secondly, this thesis studies the delay-dependent robust control of the uncertain time- varying interval delay systems containing saturated actuators. The delays are time-varying and have lower and upper bounds, saturated function is given in the form of polyhedra. Using delay-range-dependent method, the corresponding existence condition of the stable-state feedback controller is given in the form of LMIs. The domain of attraction for uncertain systems with saturation is studied. Finally, an example is given to illustrate the validity of the results.