Stabilizing discrete-time switched linear systems

Abstract: This article deals with stabilizing discrete-time switched linear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dynamics, we propose a large class of switching signals that stabilize a switched system generated by the switching signal and the given family of systems. Secondly, given a switched system, a sufficient condition for the existence of the proposed switching signal is derived by expressing the switching signal as an infinite walk on a directed graph representing the switched system. Thirdly, given a family of linear systems, we propose an algorithmic technique to design a switching signal for stabilizing the corresponding switched system.