Stabilization of a class of stochastic differential equations with Markovian switching

Abstract

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.