Stability Analysis And Control Of Switched Nonlinear Systems:Design Of State-dependent Switching Rule

As a kind of special hybrid systems,switched nonlinear systems have been widely applied in practical applications,such as network control,robot control,aircraft control,traffic control and so on.Because of the hybrid nature of switched systems and the complexity of nonlinear systems,the study of switched nonlinear systems is challenging.In recent years,there have been many research results of switched nonlinear systems under time-dependent switching strategy.However,in some cases,the switching instants will not be given in advance,a switching strategy based on the current state of the systems needs to be presented.It is necessary to study the dynamic behaviors of switched nonlinear systems under state-dependent switching.In this paper,the stability and control of switched nonlinear systems are discussed by designing state-dependent switching rules.The main contents of this paper are as follows:In Chapter 1,we introduce the research background and research status of switched nonlinear systems and state-dependent switching strategy,the main work of this paper,and some important lemmas.In Chapter 2,we mainly study the H_? tracking control of uncertain switched nonlinear systems with time delays under state-dependent switching.The stability and tracking performance of uncertain nonlinear switched systems with time delays are analyzed,respectively.By constructing Lyapunov-Krasovskii functional and state-dependent switching rules,and designing state feedback controller by matrix transformation and free-weighting matrix method,the criteria for H_? tracking performance of the systems are derived in the form of linear matrix inequalities.Finally,an example with numerical simulation is given to verify the feasibility of the conclusions.In Chapter 3,we mainly study the finite-time H_? control of switched nonlinear systems under state-dependent switching.Based on state-dependent switching strategy and multiple Lyapunov-like functions,some sufficient conditions for ensuring the solvability of the finite time H_? control problem are given whether the sliding motion occurs or not.Moreover,a state feedback controller is designed.Finally,an example is given to illustrate the effectiveness of the theoretical research method.