Stability conditions for discrete 2D switching systems, based on a multiple Lyapunov function

This paper derives sufficient conditions for the asymptotic stability of those 2D switching systems than can be represented by Roesser models in a discrete grid. Preliminary results are based on using common Lyapunov functions, giving LMI conditions for stability. To reduce the conservativeness of this preliminary approach, it is proposed in this paper to use a multiple Lyapunov function, which also gives LMI conditions. Two examples are provided to illustrate the results.