New Results on Stability and Stabilization of Markovian Jump Systems with Time Delay

This technical paper deals with the problem of stochastic stability and stabilization for a class of linear Markovian jumping systems with discrete time-varying delay. A novel delay-dependent stochastic stability criterion for Markovian delay systems is established based on new augmented Lyapunov-Krasovskii functional and delay fractioning techniques. Then a state feedback controller is designed to guarantee the stochastic stability of the resulting closed-loop system. Numerical examples are provided to illustrate the effectiveness of the proposed design approach in this paper