Robust H_∞ Control For A Class Of Continuous Dual Switching Linear System

This paper focuses on the robust stabilization of variable dual switching linear continuous time systems with exponential uncertainties,H_∞control(disturbance rejection)of variable dual switching linear continuous time systems and robust H_∞control of variable dual switching linear continuous time systems with exponential uncertainties.The variable double switching system with exponential uncertainty is a kind of system that performs deterministic switching among a limited number of Markov subsystems,it is subject to random jump and deterministic switching at the same time,and the exponential uncertainty affects the state and input matrix of the system.In this paper,the exponential uncertainty of variable dual switching system is transformed into an equivalent hybrid polyhedron model with additive norm-bounded uncertainty by using Taylor series approximation and convex polyhedron technology.Then,for the equivalent hybrid linear system model,random multi Lyapunov function method、transient performance of Markov dwell time、switching times and other transient performance are used and based on linear matrix inequality method,the optimal top-level deterministic switching law or the top-layer deterministic switching law、controller with state feedback are designed simultaneously,which makes the whole variable dual switching linear continuous time system with exponential uncertainty become robust exponential asymptotically almost sure stable.Additionally,The H_∞performance index is introduced to design a suitable top-level deterministic switching law or design a top-level deterministic switching law、a state feedback controller at the same time,so that the whole variable dual switching linear continuous time system(with exponential uncertainty)is stabilizible with H_∞disturbance attenuation levelγ(γ>0)via switching(via switched state feedback)(for all admissible uncertainties).For each problem,this paper gives the relevant research conclusions(the sufficient conditions of related research problems are given in the form of linear matrix inequality),and in some of the contents,MATLAB simulation examples are given to verify the research results.