Stability of switched Markovian jump systems with time-varying generally bounded transition rates

Abstract

This paper addresses the exponential mean-square stability for a kind of switched Markovian jump systems, which have time-varying generally bounded transition rates and mode-dependent time delay. Since these transition rates are time-varying and generally bounded, they turn out to be more practical. In fact, those existing transition rates can be treated as special cases of the proposed ones in this paper. By constructing a new Lyapunov-Krasovskii function, sufficient conditions in a tractable form are derived for the exponential mean-square stability of the considered systems. For good measure, a numerical example is given to show the efficiency and potential of the proposed method.

Conservatism reduction in robust control of Markov jump delay systems

“…An improved SLF approach (Chen et al, 2021) with the time-varying delay and time-delay bounds is proposed such that the MJDS has better H N performance. Via a new SLF, sufficient conditions with less computation are developed for the switched MJDS with time-varying generally bounded transition rates (Lu and Lie, 2021). For a nonlinear MJDS (Wang et al, 2022), a novel SLF is considered to reduce conservatism based on the delay partitioning method.…”