Stabilization For Linear Control Systems With Actuator Saturation

In real life and the actual engineering field, saturation phenomenon exists widely. For control system, there is the problem of actuator saturation, the control input once reaches a certain limit, to further increase the input will not affect the actuator output. Aimed at this phenomenon, studying the actuator saturation problem has practical significance and theoretical value, therefore this problem attracts many attentions of the researchers.The theoretical study of actuator saturation problem mainly involves the Finsler’s lemma, estimation of attraction of domain and controller design etc., the current research of these problems have achieved fruitful results, and the method has been perfect. In this article, we will further expand some methods, apply these methods to the more complex systems, and then we can get better results. The content of this article is mainly composed of the following aspects.In chapter 3, the problem of stability analysis of linear continuous time systems with actuator saturation is studied, and domain of attraction of the system is estimated. First of all, using Finsler’s lemma and Lyapunov equation to study the stability condition of the system, we get the new criterion of the stability of the actuator saturation control system. In addition, under the condition of stability, we use convex combination method and the newly introduced matrix to reduce the conservatism of estimation of domain of attraction of the system. By converting the result to linear matrix inequality, the optimization method to maximize the estimation of domain of attraction and the design scheme of the state feedback controller are presented. Finally, the simulation example verifies the results.In chapter 4, the stabilization problem of linear uncertain systems with actuator saturation is studied. First of all, basing on Finsler’s lemma and the Lyapunov function method the paper studies the stability of the system, further more, and uses a descriptor model transformation of the system to get an improved sufficient condition within the framework of linear matrix inequalities. In addition, the domain of attraction of the system is estimated by the level set and made the domain of attraction as large as possible, a convex optimization problem is designed, the result has less conservatism. Finally, a numerical example verifies the methods.In chapter 5, aimed at the saturation which plays an important role in the control theory, the sufficient conditions for the asymptotic stability of the uncertain and time-delay linear continuous systems with actuator saturation is considered. Due to the typical nonlinear characteristics of the saturation, we need to deal with saturated nonlinear item when using Lyapunov stability theory in the analysis. First of all, according to the fan zone method, the paper introduces the memory-less state feedback, moreover, applies the norm-bounded parameter uncertainty and Lyapunov function method to study the asymptotic stability conditions of the system. Secondly, under the conditions of stability, we propose a design method of memory-less state feedback controller by converting the nonlinear matrix inequality to linear matrix inequality. Finally, a two-dimensional numerical simulation example illustrates the results.In chapter 6, the stability analysis of linear discrete-time systems with actuator saturation is studied. By using convex combination method and Finsler ’s lemma, in addition, selecting saturation-dependent Lyapunov function, the paper discusses the problem of the stability analysis and the estimation of domain of attraction. By looking for a corresponding polyhedron for each ellipsoid, the method can reduce the conservatism of estimation of domain of attraction. At last, the linear matrix inequalities are given to get the domain of attraction of the system as large as possible.In the end of the paper, a summary and outlook of the study is given.