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

Recently, Mao [Automatica J. IFAC, 49 (2013), pp. 3677--3681] initiated the study the mean-square exponential stabilization of continuous-time hybrid stochastic differential equations by feedback controls based on discrete-time state observations. In the same paper Mao 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 discuss the stabilization not only in the sense of exponential stability (as Mao does in [Automatica J. IFAC, 49 (2013), pp. 3677--3681]) but also in other sense---that of H_∞ stability or asymptotic stability. We will consider not only the mean square stability but also the almost sure stability.