New Results on Stabilization of Stochastic Switching Systems Subject to Partly Available Semi-Markov Kernel

This paper investigates the stabilization issue for a class of discrete-time stochastic switching systems. The switching behavior is dominated by a semi-Markov process with finite sojourn time. Allowing for the fact that it is often difficult to get complete semi-Markov kernel (SMK) in practice, the elements in SMK of the model under study are considered to be partly accessible, which is more general than both semi-Markov model with complete SMK and Markov model with unknown transition probabilities. Sufficient stability condition is derived for the underlying system without any a priori knowledge, based on which a stabilization criterion is presented such that the closed-loop stochastic switching systems can be mean-square stable. In the end, the validity of the theoretical results is testified by a numerical example. Copyright (C) 2020 The Authors.