Robust stabilization of Markovian delay systems with delay-dependent exponential estimates

A sufficient condition for the exponential estimates of a class of Markovian systems with time delay is established for the first time in terms of the linear matrix inequality (LMI) technique. The estimating procedure is implemented by solving an LMI. The proposed condition is also extended to the uncertain case. Moreover, a state feedback stabilizing controller which makes the closed-loop system exponentially stable with a prescribed lower bound of decay rate is designed. Numerical examples are provided to illustrate the effectiveness of the theoretical results.