Asymptotical Stability in Probability for Stochastic Bilinear Systems with Markovian Switching

This paper deals with asymptotical stability in probability in the large for stochastic bilinear systems. Some new criteria for asymptotical stability of such systems have been established in the inequality of mathematic expectation. A sufficient condition for bilinear stochastic jump systems to be asymptotically stable in probability in the large in Markovian switching laws is derived in a couple of Riccati-like inequalities by introducing a nonlinear state feedback controller. An illustrative example shows the effectiveness of the method.