Prescribed-Time Stabilizaition of Linear Stochastic Parabolic Systems

This paper deals with a kind of prescribed-time stability (PTS) problem for a stochastic parabolic system with Dirichlet boundary conditions. A distributed controller is designed to ensure the stability of the system within the prescribed time (PT). It should be noted that the time of convergence is not dependent on the initial value, and it is also possible to be set in advance. Additionally, through analysis, the proof shows that the proposed distributed controller is bounded in the PT. While, the unknown external disturbances are taken into account and ensure the system’s performance in terms of H
∞
by designing a state feedback controller. Finally, the effectiveness of the proposed control method is verified through a simulation example.