Finite-time stabilisation of stochastic impulsive delayed systems with reaction-diffusion and boundary control

In this study, the problem of boundary stabilisation of stochastic impulsive delayed systems (SIDSs) with reaction-diffusion is investigated. To solve such a problem, a state feedback controller is introduced into the Neumann boundary condition. By developing a set of boundary control strategies and using average impulse interval techniques, sufficient criteria are determined to ensure that SIDSs achieve boundary stabilisation in finite time. In light of these criteria, the effects of boundary control, impulsive phenomenon, time-varying delays, and reaction-diffusion on finite-time stability are analysed. The determined stability criteria are formulated in linear matrix inequalities, which may lead to less conservative results. Numerical simulations are performed to demonstrate the feasibility of the theoretical results.