Synchronization of Lur’e-type Nonlinear Systems Over Networks of Linear Dynamical Systems: Lyapunov-based Singular Perturbation Approach

摘要

In the usual synchronization problems, the positive constants (or weights) are assigned to the edges of the given graph while the nodes are associated to dynamical systems. In contrast to this, this paper studies the synchronization problem where the edges are also dynamic. In particular, we assign asymptotically stable linear systems to the edges whereas a particular class of Lur'e-type nonlinear systems is associated to the corresponding nodes. Then, the synchronizability of the closed-loop system is analyzed based on the singular perturbation theory. The reduced model of the original system, i.e., the closed-loop system at the quasi-steady-state, corresponds to the Lur'e-type node systems with the edges treated as positive constants as usual, and a sufficient condition for the reduced model to be synchronized is given. Together with this, it is shown that the synchronization of the original singularly perturbed system is reached asymptotically if the reduced model synchronizes and the singular perturbation parameter is sufficiently small.