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, Lam, and Huang (2008); Mao, Yin, and Yuan (2007); Wu, Shi, and Gao (2010); Wu, Su, and Shi (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.