Stabilizing discrete-time switched linear systems

This article deals with stabilizing discrete-time switched lin-ear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dy-namics, 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 pro-posed switching signal is derived by expressing the switch-ing signal as an infinite walk on a directed graph represent-ing 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. Keywords Discrete-time switched linear system, asymptotic stability, multiple Lyapunov-like functions, directed graphs. 1