Stability analysis of stochastic differential equations with Markovian switching

This paper discusses the asymptotic stability of the nonlinear stochastic differential equations with Markovian switching (SDEWMSs). The equations under consideration are more general, whose transition jump rates matrix QQ is not precisely known. By using the switching process jump times to subdivide the “time” and then investigate the related sequence, we provide sufficient conditions for asymptotic stability of SDEWMSs when each subsystem is stable and a certain “slow switching” condition holds. For the general multi-dimensional linear SDEWMSs, sufficient conditions via bi-linear matrix inequalities are also proposed for the design of robust stabilization. Some examples are given to illustrate the effectiveness of our results.