L1 Gain Performance Analysis And Control Of A Class Of Discrete Double Switching Linear Positive System

A discrete-time dual-switched linear positive system is a system affected by both deterministic switching signals and Markov random switching signals.In the field of control science and engineering,the stability analysis and disturbance suppression of the switched positive system have always been a hot issue for hybrid systems.In the practical application scenario of the dual switched positive system,how to analyze the L1-gain performance of the dual switched positive system.It is urgent to study to improve the anti-interference performance of the system.Based on the premise that the disturbance suppression of discrete-time dual-switched linear positive systems is less studied,this paper constructs the Co-positive Lyapunov energy decay function and uses linear programming(LP)to obtain the guarantee that the discrete-time dual-switched positive system has a continuous residence time(PDT)constraints,the system satisfies the sufficient condition that the robustness index is almost everywhere stable(Robust-EAS).In addition,this method is extended to the L1-gain analysis of discrete-time dual-switched positive systems,and a sufficient condition for the closed-loop system to satisfy the L1 performance index χ is obtained when the robustness index is stable almost everywhere.The main work is summarized as follows:(1)The Markov transition probability of the system model selected for the discrete-time dual-switching linear positive system is the characteristic that changes with the switching of the positive subsystem(that is,it is determined by the current position of the deterministic switch),combined with the characteristics of the positive system,stochastic multilinear Lyapunov function,and Markov switching residence time,switching times and other transient performance,using the continuous residence time,when the system disturbance is guaranteed to be zero,the robust index is almost everywhere stable condition,when the system When the interference is not zero,the analysis that the system is suppressed to the L1-gain index is satisfied.And a state feedback controller design that satisfies the L1-gain performance index is designed.(2)For discrete-time dual-switched linear positive systems with exponential uncertainty,the exponential uncertainty is first transformed into a dual-switched discrete-time linear polyhedron system with additional norm bounded uncertainty,by constructing Co-positive Lyapunov The energy decay function is obtained by linear programming to ensure that the discrete-time dual-switched linear positive system with exponential uncertainty satisfies the robust exponential almost everywhere stability under the constraint of continuous residence time.In addition,this method is extended to the L1-gain analysis of discrete-time dual-switched linear positive systems with exponential uncertainty,and a sufficient condition for the closed-loop system to satisfy the L1 performance index when the robustness index is almost stable is obtained.And a state feedback controller design that satisfies the L1-gain performance index is designed.