Delay-range-dependent robust exponential stabilization for uncertain system with mode-dependent time delays and Markovian jump parameters

This paper is concerned with the problem of robust exponential stabilization for uncertain system with mode-dependent time delays and Markovian jump parameters. The delay factor is assumed to be time-varying and belongs to a given interval. The uncertainties considered in this paper are norm-bounded and possibly time-varying. A new state feedback controller with uncertain Markovian jump parameters is also designed such that the closed-loop systems are exponentially mean-square stable for all admissible uncertainties. By Lyapunov-Krasovskii functional approach, a new delay-dependent stability criteria for the exponential stability of uncertain linear system with mode-dependent time delays and Markovian jump Parameters is derived in terms of linear matrix inequalities(LMIs). A numerical example is given to illustrate the effectiveness of the method.