Stability And L2-Gain Analysis Of Nonlinear Switched Systems With Unstable Subsystems

Switched systems have been widely used in many practical applications,such as the speed control systems,the speed regulation system,the circuit system,robot control system and so on.Switched systems are important modeling tools in control theory research.Many problems have been solved by using the idea of switching in system control strategy and controller design.At present,many scholars have studied switched systems whose subsystems are all stable,and have made many related research results.In practical engineering applications,there may be sudden problems such as parts failure or sensor failure,which lead to instability of subsystems,but there are few research results on this issue.Therefore,it is of great practical significance to study switched systems with unstable subsystems.Because of the nonlinear problems in practical engineering applications,it is more difficult to analyze switched systems.In this thesis,the Takagi-Sugeno（T-S）fuzzy model is used to solve the nonlinear problems of switched systems,and the T-S fuzzy model is used to represent nonlinear subsystems in switched systems.Then the robust stability and L₂-gain of switched systems are analyzed.In this thesis,the fuzzy control theory,switched system theory and matrix theory are used to study switched nonlinear systems.The mode dependent average dwell time switching strategies and multi discontinuo-us Lyapunov functions method are used to study the robust stability and L₂-gain of nonlinear switched systems.The research content of this thesis mainly includes the following parts:（1）In the field of control,the accuracy of the system model will directly affect the analysis and running state of the system.In this thesis,aiming at the nonlinear problem in switched systems,the T-S fuzzy model and fuzzy rules of switched systems based on local linear model are adopted to solve the nonlinear problem in the system.Switched systems may change from stable subsystems to unstable subsystems due to external disturbances or sensor failures in actual operation.Therefore,it is very meaningful to consider the situation of unstable subsystems in the analysis of nonlinear switched systems in this thesis.Moreover,the influence of linear fractional parameter uncertainties on system perform-ance is considered in this thesis.Compared with norm-bounded uncertainties,the related conclusions are more general.（2）Switched T-S fuzzy systems with unstable subsystems and uncertainties are established in this thesis.Based on the systems,the stability conditions of switched T-S fuzzy systems in continuous time and discrete time are discussed respectively.For unstable subsystems,In this thesis,fast/slow switching is used for analysis,and sufficient conditions for robust stability of the switched T-S fuzzy systems are obtained by the mode dependent average dwell time switching strategies and multi discontinuous Lyapunov functions method.Compared with multi discon-tinuous Lyapunov functions method,the robust stability conditions obtained by multi-discontinuous Lyapunov functions method for switched T-S fuzzy systems are less conservative.In addition,the robust stability conditions of switched T-S fuzzy systems with different time switching strategies are given.（3）Due to the need of practical control in engineering,the systems usually needs to have good performance conditions,which means that the system must keep robustness against external uncertainties.To solve this problem,based on the stability analysis of switched T-S fuzzy systems with unstable subsystems and uncertainties in discrete time,the L₂-gain problem of switched T-S fuzzy systems is considered in this thesis.And this thesis mainly considers the L₂-gain weighted gain of the system,which can avoid staying on the subsystem with poor performance for a long time and improve the overall performance of the system.In addition,the corollaries of different Lyapunov functions methods and time switching strategies for switched T-S fuzzy systems are given.In this thesis,the effects of uncertainties,unstable subsystems and nonlinearity on the related problems of switched systems are analyzed completely,and a more flexible analysis method is adopted to reduce the stability of the system and the conservatism of L₂-gain conditions.The main conclusions of this thesis are given in the form of linear matrix inequalities,and their effectiveness is verified by numerical examples.