Stabilisation of hybrid stochastic systems with Lévy noise by discrete-time feedback control

This paper is devoted to deal with the stabilisation problems of continuous-time hybrid stochastic systems (often described by stochastic differential equations with Markovian switching) with Lévy noise by feedback controls based on discrete-time state observations. There are so far few results on the stabilisation of continuous-time hybrid stochastic systems with Lévy noise based on discrete-time state observations, despite the stabilisation of stochastic systems by discrete-time feedback controls has been investigated in general. Precisely, it is discussed the stabilisation in the sense of H∞-stability, asymptotic stability, mean-square exponential stability and almost sure exponential stability for such systems. It is also presented an upper bound on the duration τ between two consecutive state observations by means of the Lyapunov function. Two examples are given to illustrate the obtained results.