Synchronization of heterogeneous harmonic oscillators for generalized uniformly jointly connected networks

The synchronization problem for heterogeneous harmonic oscillators is investigated. In practice, the communication network among oscillators might suffer from equipment failures or malicious attacks. The connection may switch extremely frequently without dwell time, and can thus be described by generalized uniformly jointly connected networks. We show that the presented typical control law is strongly robust against various unreliable communications. Combined with the virtual output approach and generalized Krasovskii-LaSalle theorem, the stability is proved with the help of its cascaded structure. Numerical examples are presented to show the correctness of the control law.