New expectation-based conditions for almost sure exponential stability of discrete-time semi-Markovian linear systems with time-delayed control

Abstract

This paper studies almost sure exponential stability of discrete-time semi-Markovian linear systems with time-delayed control. New expectation-based sufficient conditions for almost sure exponential stability of the system are derived by employing the coupled Lyapunov function related to the sojourn time and the ergodic property of semi-Markov chains. Compared with known results on almost sure exponential stability of discrete-time semi-Markovian linear systems, the results in this paper are shown to be less conservative. At last, three numerical examples are given to illustrate the results.