Boundary control of stochastic partial differential systems with delays and Lévy noise

This paper investigates the backstepping-based boundary control approach for stabilizing the semi-linear parabolic reaction-diffusion stochastic delayed partial differential system (SDPDS) driven by Lévy noise. The invertible Volterra integral transformation is chosen for transforming the original system to the target system. Boundary control for SDPDS is designed by finding the solution of PDE involving the kernel function with the help of method of successive approximation. By $(Q,S,R)$ dissipative theory and linear matrix inequalities (LMIs), sufficient conditions are derived for proving the decreasing nature of the Lyapunov function for the target system. The result shows the system’s asymptotical stability under Neumann boundary conditions, further the stability of the target system proves the stability of the original system with control as our transformation is invertible. Finally, the proposed results are numerically validated.