Abstract: This paper introduces the concept of linear-control-based synchronization of coexisting attractor networks with time delays. Within the new framework, closed loop control for each dynamic node is realized through linear state feedback around its own arena in a decentralized way, where the feedback matrix is determined through consideration of the coordination of the node dynamics, the inner connected matrix and the outer connected matrix. Unlike previously existing results, the feedback gain matrix here is decoupled from the inner matrix; this not only guarantees the flexible choice of the gain matrix, but also leaves much space for inner matrix configuration. Synchronization of coexisting attractor networks with time delays is made possible in virtue of local interaction, which works in a distributed way between individual neighbours, and the linear feedback control for each node. Provided that the network is connected and balanced, synchronization will come true naturally, where theoretical proof is given via a Lyapunov function. For completeness, several illustrative examples are presented to further elucidate the novelty and efficacy of the proposed scheme.

Key words: linear feedback control, Lyapunov function, the Newton--Leipnik equation attractor, time delays