Mean square finite-time boundary stabilisation and H∞ boundary control for stochastic reaction-diffusion systems

Abstract

ABSTRACTIn this paper, the boundary control problem of stochastic reaction-diffusion systems (SRDSs) is studied. First, a distribution controller is designed, and a sufficient condition is established to achieve mean square finite-time stability. Then a boundary controller is proposed, and a criterion is obtained for mean square finite-time stability by using Poincaré's inequality and Gronwall's inequality. When the system is subject to external noise, a boundary controller is presented for the systems with an performance. Furthermore, a boundary controller is presented to ensure robust mean square finite-time stability of linear uncertain SRDSs. Numerical examples illustrate the validity of the theoretical results.