Practical stabilization of affine discrete-time systems by periodic switching via a time-delay approach to averaging

This article is concerned with the practical stabilization of switched affine discrete-time systems with uncertainties. We consider a time-dependent periodic switching. We transform the switched system to a time-delay system with the delays whose lengths are equal to the switching period. The time-delay system can be regarded as a perturbation of the averaged system which is supposed to be exponentially stable. The practical stability of the original system is guaranteed by the practical stability of the time-delay one. We derive sufficient input-to-state stability (ISS) conditions for the resulting time-delay system via Lyapunov-Krasovskii method in terms of linear matrix inequalities (LMIs). The upper bound on the switching period that ensures the ISS as well as the resulting ultimate bound are found from the LMIs. An example from power electronics illustrates the efficiency of results.