This paper considers the backstepping design of state feedback controllers for coupled linear parabolic partial integro-differential equations (PIDEs) of Volterra-type with distinct diffusion coefficients, spatially-varying parameters and mixed boundary conditions. The corresponding target system is a cascade of parabolic PDEs with local couplings allowing a direct specification of the closed-loop stability margin. The determination of the state feedback controller leads to kernel equations, which are a system of coupled linear second-order hyperbolic PIDEs with spatially-varying coefficients and rather unusual boundary conditions. By extending the method of successive approximations for the scalar case to the considered system class, the well-posedness of these kernel equations is verified by providing a constructive solution procedure. This results in a systematic method for the backstepping control of coupled parabolic PIDEs as well as PDEs. The applicability of the new backstepping 查看全文>>