Abstract
Stabilizability and stabilization are considered on a first order system whose dynamics stochastically changes subject to a Markov chain. Although a necessary and sufficient condition is known for the stabilizability, it is not convenient in the sense that it can be checked only through minimization of a non-convex function. In this paper, a more convenient sufficient condition is presented, which is based on conditional variance. It is also shown that a control law simpler than the known one stabilizing the system when the presented condition is satisfied. These results are considered to be useful for better understanding of stabilizability and stabilization of such systems.
