School of Mathematics, Hefei University of Technology; Department of Mathematics and Physics, Hefei University

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.