Reachable Set Estimation for Discrete-time Periodic Piecewise Systems

This paper investigates the reachable set estimation problem for discrete-time periodic piecewise systems subject to bounded-peak disturbances for the first time. Based on the periodic linear-interpolative formulation, the discrete time-scheduling Lyapunov functions with non-jumping or jumping modes are constructed to develop criteria of reachable set estimation that can ensure the asymptotic stability and reachability of the investigated system. Moreover, an index optimizing the bounding region of the desirable reachable set is given via resorting to the ellipsoid technique, and their results are compared. Finally, numerical examples are given to validate the effectiveness of the proposed results.