Stability Study Of Double-switched Discrete Linear Positive Systems

Dual switching positive systems are a kind of dual switching systems whose system states is always in positive quadrant.They are composed of a limited number of positive subsystems and a new internal driving mechanism controlled by two different switching signals,and have the characteristics of both positive and dual switching systems.Dual switching positive systems are widely used in practical system modeling,such as wind power generation,network control and other fields.Because it is necessary to consider not only the complex dynamic behavior of the dual switching system,but also the positive property of the system,Which leads analyze the dual switching positive system difficultly.Therefore,the analysis of dual switching positive systems is not only of great theory significance,but also of wide practical value.This paper is based on the existing research results,the stability of dual switching positive systems is studied.The main works of this paper includes the following:(1)This paper deals with a dual switching discrete-time linear positive system with deterministic and stochastic switching signals and positive subsystems.By using stochastic multiple linear co-positive Lyapunov function and the energy attenuation principle,under the condition that the deterministic switching signal satisfies the constraint of average dwell time and per-designed,a sufficient condition for mean square stability of dual switching discrete-time linear positive system is deduced respectively.(2)This paper deals with a dual switching discrete-time linear positive system with deterministic and stochastic switching signals and positive subsystems.By using stochastic multiple linear co-positive Lyapunov function,the energy attenuation principle and the transient analysis of Markov chains,under the condition that the deterministic switching signal satisfies the constraint of the per-designed,a sufficient condition for exponentially almost sure stability of dual switching discrete-time linear positive system is presented.(3)This paper deals with a dual switching discrete-time linear positive system with deterministic and stochastic switching signals and positive subsystems.By using stochastic multiple linear co-positive Lyapunov function,the transient analysis of Markov chains and designing of deterministic switching signal with average dwell time,a sufficient condition for globally asymptotically stable almost surely of dual switching discrete-time linear positive system is deduced.