Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay

Abstract

This paper deals with the robust finite-time stability and stabilization problems of uncertain stochastic delayed jump systems, where the uncertainty is in the form of additive perturbations and exists in the drift and diffusion sections simultaneously. Though perturbation, time-varying delay and Brownian motion existing at the same time, two conditions checking its robust finite-time stability are proposed by a mode-dependent parameter approach, which are different from some existing methods. Based on the proposed results, sufficient conditions for the existence of the state-feedback controller are provided with LMIs, which could be solved directly. It is seen that all the features of the underlying system such as time-varying delay, perturbation, diffusion, mode-dependent parameters and uncertain transition rate matrix play important roles in the system analysis and synthesis of finite-time stability. Finally, numerical examples are used to demonstrate the effectiveness and superiority of the proposed methods.