Inner-approximations of domains of attraction for discrete-time switched systems with arbitrary switching

In this paper, we propose an iteration method to compute inner-approximations of the domains of attraction for discrete-time switched systems with arbitrary switching. Starting from an initial estimated domain of attraction, which can be obtained by previous methods in the literatures, we firstly present a theoretical framework for obtaining a larger one via iteratively computing common Lyapunov-like functions. Successively, the theoretical framework is under-approximatively realized by using sums of squares programming, associated with a coordinate-wise iteration idea. Further, we propose an alternative method to obtain an initial estimated domain of attraction. Finally, two examples with comparisons are illustrated to show the advantages of our method.