Study On Stability Of Variable Dual Switching Continuous-tiem Nonlinear Systems

Switching dynamic system is a special kind of hybrid system,which consists of a family of subsystems and switching strategies that describe the relationship between them.According to different switching drive mechanisms,switching systems can be divided into two types: deterministic switching systems and random switching systems.With the complication of control system in practical engineering field,only deterministic switching system or stochastic switching system can be used to model,and its internal driving mechanism cannot be accurately described.Some scholars have proposed a new type of system,dual switching system,which has both deterministic switching signals and random switching signals.In this paper,the stability of variable dual switched continuous-time nonlinear systems and variable dual switched continuous-time linear systems are studied.Specifically,the global asymptotic stability almost sure(GAS.a.s.)and exponential stability almost sure(ES.a.s.)of the variable dual switched systems are studied respectively.The main research contents are summarized as follows:Based on the transient performance of stochastic processes and stochastic Multilyapunov function,the global asymptotic stability almost sure and exponential stability almost sure of variable dual switched continuous-time nonlinear systems are studied.In order to expand some new aspects of this system,our main contributions nonlinear systems are: designing deterministic switching signals,constructing corresponding Lyapunov functions for N Markov subsystems,and selecting the minimum expected value as the deterministic switching signal;Two sufficient conditions are givn respectively for the global asymptotic stability almost sure(GAS.a.s.)and eoponential stability almost suer(ES.a.s.)of variable dual switched continuous-time nonlinear systems.In our research,the transfer rate matrix of stochastic Markov processes in our study is not fixed,but varies when a deterministic switching take place.By analyzing the stability of nonlinear,we will apply the same method to study the stability of variable dual switched continuous-time linear systems for linear cases.Two aspects are given: the Lyapunov functions of the minimum expected value of N Markov subsystems is selected as the deterministic switching signal;At the same time two sufficieng conditions are given for the globally asymptotically stable almost sure(GAS.a.s.)and exponentially stable almost sure(ES.a.s.)of the variable dual switched continuous-time linear system.Finally,MATLAB simulation software is applied to verify the rationality of the two sufficient conditions givn by the variable dual switching continuous-time nonlinear systems and the variable dual switching continuous-time linear system,and the verification is successful.