Stability analysis of discrete-time semi-Markov jump linear systems with partly unknown semi-Markov kernel

This paper is concerned with the problems of stability analysis and stabilization synthesis for a class of discrete-time semi-Markov jump linear systems. The novel sufficient stability conditions for such systems are obtained, in which the sojourn times are allowed to be unbounded, and thus these conditions are applicable to discrete-time Markov jump linear systems. Moreover, by truncating the sojourn times of switching process to be bounded, the numerically testable existence conditions of stabilizing controller for the resulting closed-loop systems with partly unknown semi-Markov kernel are obtained. An example is given to illustrate the effectiveness of our results. (C) 2020 Elsevier B.V. All rights reserved.