Stability of Discrete-Time Regime-Switching Dynamic Systems with Delays

Abstract

This work focuses on stability of regime-switching discrete-time systems with delays. Two-time-scale formulation is used for the purpose of reduction of complexity. It is demonstrated that associated with the original system, there is a limit system that is a switching diffusion process. An interesting problem is concerned with if the stability of the limit switching diffusion process can be carried over to the original system. This question is answered in the article. Furthermore, path excursion, mean recurrence time, and the associated error bounds are considered.