Stabilization Design Of Two Classes Of Switched Linear Systems With Actuator Saturation

Switched systems can accurately describe the actual model,which have important theoretical research value and a wide range of practical application background.Switched systems theory research has become an international frontier direction in hybrid system theory research.Many practical engineering systems such as aerospace,automotive industry,chemical process,traffic transmission process,computer control systems,communications industry and so on can be modeled as switched systems.In addition,actuator saturation is one of the common nonlinear problems in practical control systems.In industrial systems,common devices for actuator tasks are limited in use.If the effect of saturation limitation of the corresponding controller is not considered,or if the saturation treatment is not carried out,it will directly reduce the systems operation performance,and even destroy the stability of the systems.Therefore,it has great scientific significance and wide practical application value to solve the problems of actuator saturation in the systems.When there is actuator saturation in the switched systems,the coexistence and interaction of continuous dynamic,discrete dynamic and saturation nonlinearity make the dynamic behavior of the saturation switched systems more complex than that of the general switched systems or saturation systems.The operating mechanism of the systems is far from clear,and a large number of analysis and synthesis problems need to be solved urgently.Therefore,this paper mainly studies the stabilization design of two classes of switched linear systems with actuator saturation.The main contents of this paper are as follows:In Chapter 1,firstly,the switched systems are summarized.Then,the research significance,research methods and research progress of the saturated systems are summarized.Next,the research methods and research progress of the saturated switched systems are summarized.Finally,the main research contents of this paper are stated.In Chapter 2,based on the synchronously design of the dwell time switching signal and stabilization controllers,the exponential stabilization of continuous-time switched linear systems with actuator saturation is studied.The existing results on this issue are usually obtained under the premise of all subsystems are stabilizable.In this chapter,we assume that the subsystems of the switched system includes both stabilizable subsystems and unstabilizable subsystems.By using a class of multiple time-varying Lyapunov function methods,we synchronously design the stabilization controllers and dwell time switching signal,constrain the “energy” growth rate of the Lyapunov function,and let the “energy” of the Lyapunov function decreases at adjacent switching points.The sufficient conditions for exponential stabilization of the continuous-time switched systems are obtained,and the corresponding attractive region is given.Then,we obtain the existence conditions of the stabilization controllers based on linear matrix inequality.In order to expand the estimation of attractive region of the systems,the optimization problem constrained by linear matrix inequality is proposed.The results obtained above can also be degraded to the case that all subsystems are stabilizable,which is considered in this chapter and the corresponding constraint optimization problem of attractive region are given.When asynchronous switching occurs in a continuous-time switched linear system with actuator saturation,the exponential stabilization problem is studied by applying the above obtained results,and the optimization problem of the attractive region constrained by linear matrix inequality under asynchronous switching control is proposed.Finally,two simulation examples are used to verify the effectiveness of the proposed method in this chapter.In Chapter 3,based on the synchronously design of dwell time switching signal and stabilization controllers,the exponential stabilization of the discrete-time switched linear systems with actuator saturation is studied.In this chapter,we also assume that the subsystems of the switched systems includes both stabilizable subsystems and unstabilizable subsystems.By constructing a class of multiple time-invarying Lyapunov functions,the stabilization controllers and dwell time switching signal are designed synchronously.The sufficient conditions of exponential stabilization of the systems and the corresponding attractive region are obtained.The existence conditions of the stabilization controllers based on linear matrix inequality are obtained.In order to maximize the estimation of attractive region of the systems,the optimization problem constrained by linear matrix inequality is proposed.The above results can be degraded to the case that all subsystems are stabilizable,which is considered in this chapter and the corresponding constraint optimization problem of attractive region is obtained.When asynchronous switching occurs in the discrete-time switched linear systems with actuator saturation,the above results are used to study the exponential stabilization problem for these systems.The optimization problem of the attractive region constrained by linear matrix inequality under asynchronous switching control is proposed.Finally,the effectiveness of the proposed method in this chapter is verified by simulation examples.In Chapter 4,the work done in this paper is summarized,and the next research problems are pointed out.