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 tau between two consecutive state observations. However, it is due to the general technique used there that the bound on tau is not very sharp. In this paper, we will be able to establish a better bound on tau 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-infinity stability or asymptotic stability. We will consider not only the mean square stability but also the almost sure stability.