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

Mei, Chunhui and Fei, Chen and Fei, Weiyin and Mao, Xuerong (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). pp. 313-323. ISSN 1751-8644

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    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 τ is also given in this study. Finally, a numerical example is given to illustrate the proposed theory.