Boundary control of stochastic partial differential systems driven by Lévy noise

Abstract This paper focuses on stabilizing the unstable semi-linear parabolic stochastic partial differential system (SPDS) driven by Lévy noise. The boundary control for SPDS is designed using backstepping method through Volterra integral transformation. With the help of linear matrix inequality and Lyapunov analysis, the stability of the transformed system has been presented. Since the selected transformation is invertible, the stability of the transformed system implies the stability of the original system with designed control. The result guarantees the system’s asymptotic stability under Neumann boundary conditions. Finally, the effectiveness of the proposed results are validated through numerical examples by demonstrating the stabilizability of the system under designed control.