Synchronization and stabilization of coupled unstable systems with delayed couplings

Abstract

This paper considers the simultaneous stabilization problem for multiple identical unstable systems using network synchronization. In particular, we attempt to design a coupling such that all systems in networks are synchronized, and each system is stabilized at the equilibrium point. The proposed coupling consists of a linear combination of the projective synchronization errors with a constant scaling factor and the delayed values. To realize the simultaneous stabilization based on synchronization, we consider the local stability of both the equilibrium point of a system in the networks and the synchronization errors between the system and others. From the stability analysis, we show that synchronization for mutual-coupled systems with the proposed coupling can lead to the simultaneous stabilization of This result also supports the usefulness of the proposed scheme.