Stabilization of continuous-time hybrid stochastic differential equations by discrete-time feedback control

In this paper we are concerned with the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations (also known as stochastic differential equations with the Markovian switching) by discrete-time feedback controls. Although the stabilization by continuous-time feedback controls for such equations has been discussed by several authors (see e.g. Ji and Chizeck, 1990, Mao et al., 2008, Mao et al., 2007, Wu et al., 2010 and Wu et al., 2012), there is so far no result on the stabilization by discrete-time feedback controls. Our aim here is to initiate the study in this area by establishing some new results.