Stability And H_? Control Of A Class Of Nonlinear Singular Switched Systems

With the continuous development of science and technology,more and more attention has been paid to the study of nonlinear singular systems.For example,power systems,population models,and economic systems all have nonlinear singular systems.As the most typical representative of the hybrid system,the switched system is composed of multiple subsystems and the switching rules acting on these subsystems.If the subsystems of the switched system contain a nonlinear singular system,it is called nonlinear singular switched system.The study of nonlinear singular switched systems has important theoretical significance and practical value.In this paper,the state undecomposed method combined with multi-Lyapunov function method and the average dwell time method is used as a research tool to study several control problems of the nonlinear singular switched systems.The main contents are summarized as follows:1.The multi-Lyapunov function method and the state undecomposed method are used to study the exponential stability andH_?control problems of a class of nonlinear singular switched systems,and the corresponding state-dependent switching laws are designed.Under the given state feedback conditions,the sufficient conditions for the corresponding closed-loop systems to be exponentially stable andH_?exponentially stable are obtained.2.The finite-time stability and finite-timeH_?control problems of nonlinear singular switched systems are studied by using the multi-Lyapunov function method and the state undecomposed method.The corresponding state-dependent switching laws are designed,and the sufficient conditions for the closed-loop systems to be finite-time stable andH_?finite-time stable are obtained.3.The exponential stability of the nonlinear singular switched systems is studied by using the average dwell time method and the state undecomposed method.Under suitable state feedback conditions,the sufficient conditions of exponential stability andH_?exponential stability of the corresponding closed-loop systems are obtained.And we also design a switching law dependent on dwell time.4.The finite-time control problem of nonlinear singular switched systems is studied by using the average dwell time method and the state undecomposed method.Under appropriate state feedback conditions,the corresponding closed-loop systems'sufficient conditions of finite-time stability andH_?finite-time stability are obtained,and a switching law dependent on dwell time is designed.In each part,we use numerical simulation examples to verify the feasibility of the results.