Stabilization in Distribution by Delay Feedback Control for Hybrid Stochastic Differential Equations

This article is concerned with the design of a feedback control based on past states in order to make a given unstable hybrid stochastic differential equation (SDE) to be stable in distribution (stabilization in distribution). This is the first article in this direction. Under the global Lipschitz condition on the coefficients of the given unstable hybrid SDE, we will show that the stabilization in distribution can be achieved by linear delay feedback controls. In particular, we discuss how to design feedback controls in two structure cases: state feedback and output injection.