Analysis and adaptive control for robust H_∞ synchronization of complex coupled parabolic networks

This paper delves into the robust H_∞ synchronization problem for a type of complex coupled parabolic networks (CPNs). Considering the time delay and spatial diffusion that might exist in the nodal dynamics, a complex CPN with delayed state coupling and spatial diffusion coupling is established by semi-linear parabolic partial differential equations (PDEs). An H_∞ synchronization criterion is derived for the considered complex CPNs utilizing the Green's formula, the boundary conditions and the gradient operations. Furthermore, a distributed adaptive control scheme is presented to guarantee the H_∞ synchronization for CPNs with delayed state and spatial diffusion couplings. Finally, two numerical examples are utilized to validate the correctness of the obtained control criteria and to illustrate the advantages of the presented approaches.