Stabilization of hybrid systems by feedback control based on discrete-time state and mode observations

Recently, Mao [1] proposed a kind of feedback control based on discrete time
state observations to stabilize continuous-time hybrid stochastic systems
in mean-square sense. We find that the feedback control there still depends
on the continuous-time observations of the mode. However, it usually costs to
identify the current mode of the system in practice. So we can further improve
the control to reduce the control cost by identifying the mode at discrete times
when we make observations for the state. In this paper, we aim to design such
a type of feedback controls based on the discrete-time observations of both
state and mode to stabilize the given unstable hybrid stochastic differential
equations (SDEs) in the sense of mean-square exponential stability. Moreover,
a numerical example is given to illustrate our results.