The Study On The Stability Of Variable Dual Switching Discrete-time Linear System

In this paper,the variable dual switching discrete-time system with both deterministic and stochastic switching signals and the interaction between the two kinds of switching signals is taken as the research object.The exponentially almost sure stability of the system is analyzed by using the stochastic multi-lyapunov function and the energy attenuation principle under the condition that the deterministic switching signal satisfies the constraint of persistent dwell time and average dwell time respectively.This topic is a powerful expansion of the research of dual switching system at home and abroad,which has important theoretical significance and practical application value.The main innovative works of this paper are as follows:(1)This paper deals with a variable dual switching system with both deterministic and stochastic switching co-existing and interacting.By using the stochastic multi-lyapunov function and the energy attenuation principle,under the condition that the deterministic switching signal satisfies the constraint of average dwell time,a sufficient condition is given for the exponentially almost sure stability of the variable dual switching discrete-time linear system.Then,based on the results of variable dual switching discrete-time linear system,we extend the research scope to the nonlinear case and obtain a sufficient condition for the exponentially almost sure stability of variable dual switching discrete-time nonlinear system by using the same method.(2)By using the stochastic multi-lyapunov function?the transient characteristics of stochastic Markov chain and the energy attenuation principle,under the condition that the deterministic switching signal satisfies the constraint of persistent dwell time investigated the exponentially almost sure stability of variable dual switching discrete-time linear system with exponential uncertainty.Finally,a sufficient condition for the exponentially almost sure stability of the variable dual switching discrete-time linear system is given in the form of linear matrix inequality.