Boundary control for passivity of multiple state or spatial diffusion coupled parabolic complex networks with and without control input constraint

In this paper, the passivity for multiple state or spatial diffusion coupled parabolic complex networks (PCNs) with and without control input constraint are considered. Firstly, we investigate the passivity of multiple state coupled PCNs without control input constraint, and some relevant criteria are derived by devising suitable boundary controller and making use of Lyapunov function method. What is more, the control input constraint for multiple state coupled PCNs is also taken into account, and several sufficient conditions are also derived so as to assure the existence of the boundary controller. In addition, the passivity of multiple spatial diffusion coupled PCNs with and without control input constraint is also investigated. Finally, two simulation examples are presented to verify the validity of the obtained criteria.