Stabilization of a class of stochastic differential equations with Markovian switching

Stability of stochastic differential equations with Markovian switching has been studied quite extensively for a number of years, for example, by Basak et al. (J. Math. Anal. Appl. 202 (1996) 604-622), Ji and Chizeck (IEEE Trans. Automat. Control 35 (1990) 777-788), Mariton (Jump Linear Systems in Automatic Control, Marcel Dekker, New York, 1990), Mao et al. (Stochastic Process. Appl. 79 (1999) 45-67; Bernoulli 6 (2000) 73-90) and Yuan and Lygeros (in: R. Alur, G. Pappas (Eds.), Hybrid Systems: Computation and Control, Seventh International Workshop, HSCC 2004, Lecture Notes in Computer Science, vol. 2993, Springer, Berlin, 2004, pp. 646-659). By contrast, the problem of designing controllers to stabilize systems of this type has received relatively little attention. In this paper we study the problem of mean square exponential stabilization for a class of stochastic differential equations with Markovian switching.