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 τ is also given in this study. Finally, a numerical example is given to illustrate the proposed theory.
- asymptotic stability
- discrete time system
- differential delay equations
- continuous time systems
Mei, C., Fei, C., Fei, W., & Mao, X. (2020). Stabilisation of highly non-linear continuous-time hybrid stochastic differential delay equations by discrete-time feedback control. IET Control Theory and Applications , 14(2), 313-323. https://doi.org/10.1049/iet-cta.2019.0822