Stabilization of Hybrid Systems by Feedback Control Based on Discrete-Time State Observations

Recently, Mao [19] initiates the study the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. Mao [19] also obtains an upper bound on the duration τ between two consecutive state observations. However, it is due to the general technique used there that the bound on τ is not very sharp. In this paper, we will be able to establish a better bound on τ making use of Lyapunov functionals. We will not only discuss the stabilization in the sense of exponential stability (as Mao [19] does) but also in other sense of H∞ stability or asymptotic stability. We will not only consider the mean square stability but also the almost sure stability.