Estimation and synthesis of reachable set for switched linear systems

This paper focuses on the problems of reachable set estimation and state-feedback controller design for discrete-time switched linear systems under bounded peak disturbances. For the reachable set estimation problem, a Lyapunov-based inequality is developed based on the multiple Lyapunov strategy. By choosing appropriate Lyapunov functions, the ellipsoidal reachable set estimation conditions of discrete-time switched linear systems are obtained. In order to make the estimated ellipsoids as small as possible, three optimization approaches are proposed. Specifically, the Genetic Algorithm is used to search for the optimal parameters satisfying the obtained reachable set estimation conditions. In addition, the state-feedback controller design problem for discrete-time switched linear systems is considered. The function of the controller is to manipulate the reachable set of the closed-loop system to lie within a given ellipsoid or make the reachable set small. Finally, the effectiveness of the obtained results is verified through some numerical examples.