2017 年 83 巻 846 号 p. 16-00467
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 systems in the networks. The effectiveness of the proposed coupling is demonstrated through examples of coupled rotary inverted pendulums with the proposed coupling. The simulation results show that it is impossible either to stabilize each system or to synchronize all coupled systems if there is no delay in the coupling, but due to the existence of delay the simultaneous stabilization and synchronization can be achieved in the networks. In addition, it is worth remarking that the stabilization and synchronization of systems with the proposed coupling are not subject to the so-called odd number limitation. Finally, we show an experimental result for two rotary inverted pendulums coupled with the proposed coupling. This result also supports the usefulness of the proposed scheme.
