Fuzzy Control And Filtering Of Switched Nonlinear Systems

In practice,many systems and processes can be modeled as switched systems to study,such as the chaos generator of electronic circuit,the DC-DC power converter,the robot control and so on.Therefore,the study of switched systems has a profound application background.With the development of switched systems,the switching idea is also widely used to study other systems.For example,based on the switching method,some work have studied the control problem of networked control systems or the finitetime synchronization problem of coupled neural networks,and so on.So the study about switched systems is of great significance for the development of other systems.Based on the fact that the nonlinearity generally exists in many practical systems,this dissertation studies the control and filtering problems of switched nonlinear systems.Because of the nonlinearity,it is difficult to analyze the switched nonlinear systems directly.In order to overcome this problem,the well-known Takagi-Sugeno(T-S)fuzzy model is used in this dissertation to represent each nonlinear subsystem of the switched nonlinear systems.By using the T-S fuzzy mode,the switched nonlinear systems are modeled as the switched T-S fuzzy systems.In this dissertation,together the multiple Lyapunov functions approach with time-dependent analysis method,the switched system theory,nonlinear system theory,fuzzy control theory and matrix theory are used to study the fuzzy control and filtering problems of switched nonlinear systems.The main contents and originalities of this dissertation are given as follows:1.The fuzzy asynchronous control problem of switched nonlinear systems is studied in this dissertation.Firstly,the fuzzy asynchronous H_?control problem of switched nonlinear systems is studied.Then,the fuzzy asynchronous control problem of impulsive switched nonlinear systems is investigated.In the end,the fuzzy asynchronous control problem of switched nonlinear systems with unstable subsystems is studied.By using the fuzzy Lyapunov functions approach and the mode-dependent average dwell time technique,the asynchronous stabilization conditions for these three different problems are obtained,which have less conservativeness.All the conditions can be expressed as a set of linear matrix inequalities.The desired controllers can be constructed by solving these linear matrix inequalities.2.In this dissertation,a new performance index is proposed,which is the mixed H_?and passive performance index.This new performance index contains the weighted H_?performance index and the passive performance index.Based on this new performance index,the mixed H_?and passive filtering problem of switched nonlinear systems is studied in both continuous-time and discrete-time contexts.By using the multiple Lyapunov functions approach and the average dwell time method,and introducing some slach matrices,sufficient conditions for the existence of admissible mixed H_?and passive filters for these two different switched nonlinear systems are obtained.All the conditions can be expressed as a set of linear matrix inequalities.The desired mixed H_?and passive filters can be constructed by solving these linear matrix inequalities.3.By proposing a novel performance index which can be viewed as the extended dissipativity performance index,this dissertation studies the weighted H_?,2-H_?,passive and dissipative control problems of switched nonlinear systems in a unified framework.Based on this new performance index,and by using the multiple Lyapunov functions approach and the average dwell time technique,more general stabilization conditions are obtained.All the stabilization conditions are expressed in terms of linear matrix inequalities.The state feedback controllers can be constructed by solving these linear matrix inequalities.Under the constructed controllers,the closed-loop switched nonlinear systems are globally uniformly asymptotically stable and satisfy the novel performance index.4.The H_?filtering problem of switched nonlinear systems with stable and unstable subsystems is studied in this dissertation.If the switched system contains unstable subsystems,the filtering error system obtained by the augmentation technique will contain unstable filtering error subsystems.When the switched system switches to the unstable subsystem,the states of the filtering error system will become divergent.As a result,the output of filters can not well estimate the actual output signal.To overcome this problem,a set of mode-dependent filters of a Luenberger-like observer type are constructed.Through designing appropriate filter gains,the filter error system do not contain any unstable filtering error subsystems even if the existence of unstable subsystems in the switched nonlinear systems.The multiple Lyapunov functions approach and modedependent average dwell time technique are employed to solve the H_?filtering problem.New sufficient conditions are obtained to ensure the filtering error system to be asymptotically stable with a prescribed H_?performance index.These conditions are expressed as a set of linear matrix inequalities.Moreover,the desired H_?filters can be constructed by solving these linear matrix inequalities.5.By constructing a novel switching Lyapunov function,the robust stabilization problem for a class of polytopic uncertain switched nonlinear systems without stable subsystems is investigated in this dissertation.This new switching Lyapunov function has the “switching-decreasing” property at switching instant.In order to obtain less conservative results,by combining this new switching Lyapunov function with the parameterdependent stability idea,the switching decreasing parameter-dependent Lyapunov functions are further proposed to investigate the studied switched nonlinear systems.By using the switching decreasing parameter-dependent Lyapunov functions approach and the maximum average dwell time technique,sufficient conditions are obtained to guarantee the studied switched nonlinear systems to be asymptotically stable.All the conditions are expressed as a set of linear matrix inequalities.