Stability of stochastic differential equations with Markovian switching

Stability of stochastic differential equations with Markovian switching has recently received a lot of attention. For example, stability of linear or semi-linear type of such equations has been studied by Basak et al. (1996, J. Math. Anal. Appl. 202, 604–622), Ji and Chizeck (1990, Automat. Control 35, 777–788) and Mariton (1990, Jump Linear Systems in Automatic Control, Marcel Dekker, New York). The aim of this paper is to discuss the exponential stability for general nonlinear stochastic differential equations with Markovian switching.