Exponential Stabilization in Mean Square of Stochastic Systems with Delay and Markovian Switching via State-Feedback

Exponential stabilization in mean square is investigated for a class of stochastic systems, where Markovian switching and time-varying delay is introduced. In order to guarantee the exponential stability in mean square for the system, a sufficient condition is derived using the method of Liapunov function and LMI. Furthermore, a kind of desirable gain matrix is designed to make the system the exponential stability in mean square by the state feedback. Finally, when the Markov chain goes around all its modes, a mode-independent gain matrix is presented to guarantee the exponential stability in mean square for this system