Exponential Stability Study Of Double-switched Continuous Linear Positive Systems

As a new type of hybrid system,the dual-switching system(also called switched Markov jump system)has been widely used in practical engineering due to the simultaneous existence of deterministic switching signals and random switching signals.The positive system is a special kind of dynamic system.Because its state trajectory is strictly constrained in the non-negative region of the state space,it also has a status that cannot be ignored in the actual engineering field.At the same time,stability,as the most basic performance requirement of a system,has been widely concerned by scholars.The research object of this subject is a dual-switching continuous linear positive system.Compared with general dual-switching systems,this type of system has both the properties of a dual-switching system and a positive system.The complex characteristics induced by the interaction of the two properties make it research is more challenging.We will further study the exponentially stability of such systems on the basis of existing research results,and make certain efforts to enrich the theoretical knowledge of dynamic systems.1.Analyze the exponentially mean square stability of the dual-switching continuous linear positive system.Based on the transient performance of the Markov process,using the principle of energy attenuation,the corresponding multi-Lyapunov functions is constructed for N Markov subsystems at the same time,and the minimum expected value is selected as the deterministic switching signal.A new theorem on the exponentially mean square stability of a dual-switched continuous linear positive system is derived.A numerical example is given,and Matlab simulation software is used to verify the effectiveness of the selected switching signal and the accuracy of the theorem.2.Analyze the exponentially almost-sure stability of the dual-switching continuous linear positive system.Based on the transient performance of the Markov process,the minimum dwell time method and the average dwell time method are used respectively,and the deterministic switching signal is designed based on the average dwell time.Two new theorems are deduced that the index of the dual-switched continuous linear positive system is exponentially almost-sure stable.Two numerical examples are given,and Matlab simulation software is used to verify the effectiveness of the selected switching signal and the accuracy of the theorem.