Stabilisation of highly non‐linear continuous‐time hybrid stochastic differential delay equations by discrete‐time feedback control

Abstract

In this study, the authors consider how to use discrete-time state feedback to stabilise hybrid stochastic differential delay equations. The coefficients of these stochastic differential delay equations do not satisfy the conventional linear growth conditions, but are highly non-linear. Using the Lyapunov functional method, they show that a discrete feedback controller, which depends on the states of the discrete-time observations, can be designed to make the solutions of such controlled hybrid stochastic differential delay equations asymptotically stable and exponentially stable. The upper bound of the discrete observation interval is also given in this study. Finally, a numerical example is given to illustrate the proposed theory.