Research On Fuzzy Control Theory Of Nonlinear Switched Systems With Unstable Subsystems

The nonlinear switched system consists of several nonlinear subsystems and switching laws to govern the subsystems.Such system has widely application backgrounds in the engineering control applications,such as automobile variable speed systems,aircraft control systems,machine servo systems and so on.Most of the existing research results are mainly focused on the case when all the subsystems are stable.However,in practical applications,the subsystems may become unstable due to sensor noise,equipment failure and other reasons.Therefore,the significance of studying the nonlinear switched systems with unstable subsystems can also not be ignored.Stability analysis,control and filtering problems are the research emphasis of control theory for the nonlinear switched system.However,the nonlinearity of subsystems will make it difficult to analyze the switched system directly.Therefore,this dissertation utilizes the Takagi-Sugeno(T-S)fuzzy models to dispose the nonlinear subsystems,and further studies the stability analysis,control and filtering problems of nonlinear switched systems with unstable subsystems.The main works of this dissertation can be divided into the following five aspects:(1)Aiming at the stability problem of nonlinear switched systems with subsystems are all unstable,a new”stable switching”and divergence time concepts are introduced in this dissertation.The system can absorb the state divergence of the”unstable-switching”by activating the”stable-switching”for sufficiently long.Based on that,a more general stability condition under bounded maximum average dwell time switching is obtained.Compared with the traditional dwell time and maximum average dwell time stability conditions,the stability condition obtained in this dissertation can eliminate the limitation of the minimum dwell time and expand the range of switching signals.(2)The model-dependent average dwell time uniform stability problem for nonlinear switched systems is investigated.The nonlinear switched systems can be composed of arbitrary stable or unstable subsystems.Firstly,a”switching stability”concept is proposed,which has no directly relationship to the stability or the switching strategy of the subsystems.Based on the”switching stability”,the subsystems are reclassified as”switching-stable”and”switching-unstable”,and while the stability condition of the switching signal will be confirmed by the activation time ratio between them.In addition,different from the existing unified stability conclusions,the unstable subsystems in this dissertation can switch between each others,and can also arbitrarily adopt the slow or fast switching strategy.(3)Consider the asynchronous H_?control problem for switched systems,in the real-life application,the state of closed-loop subsystem may be divergent in the asynchronous time interval.Therefore,the asynchronous control problem can be regarded as a case for switched systems with unstable subsystems.Based on the assumption that the switching instants can be detected instantaneously online,the asynchronous and synchronous controller are designed separately in this dissertation.Then,by utilizing a novel time-varying fuzzy Lyapunov function,the non-weighted asynchronous H_?controller is established.Compared with the traditional controller forms or the fuzzy Lyapunov function,the proposed controller in this dissertation is proved to be less conservative.(4)Consider the asynchronous H_? filtering for the switched system,the state of the filtering error system may be divergent in the asynchronous time interval.Thus,it can also be viewed as a case for switched systems with unstable subsystems.Based on the similar design idea as asynchronous H_?controller,this dissertation derives out the non-weighted asynchronous H_?filter for nonlinear switched systems,and has compared it with the traditional asynchronous filter design methods.(5)For the general H_?filtering problem for the switched system,the filter error system will be divergent when the corresponding subsystem is unstable.Under this circumstances,the filter may be affected to estimate the original output.This dissertation has extended the uniform stability condition to the filter design,and first time investigated the weighted uniform H_?filtering problem for the nonlinear switched systems composed of arbitrary stable or unstable subsystems.