Finite-time stabilization of stochastic delay reaction-diffusion systems

In this paper, the problem of finite-time stabilization of stochastic delay reaction-diffusion systems (SDRDSs) is investigated. The finite-time controller is designed without using the sign function. Then, applying the stochastic finite-time stability lemma, utilizing Lyapunov-Krasoviskii functional method and Itö formula, a sufficient condition is derived which guarantees the finite-time stabilization of the stochastic delay reaction-diffusion systems under the designed controller. The effect of the spatial domain on the finite-time stabilization can also be observed from this sufficient condition. At last, an example is offered to verify the effectiveness of the controller.