Dual-observer-based event-triggered state synchronization for discrete-time output-coupled neural networks under Round-Robin protocol

Aiming at the state master-slave synchronization problem of discrete-time output-coupled neural networks (OCNNs), this study proposes a novel control framework. Deviating from the existing studies, this study aims at the constraint that the output state cannot obtain all neuron state information, innovatively constructs full-dimensional observers in the master/slave system respectively to realize state reconstruction, which solves the problem of missing reference trajectory caused by incomplete state information of the master system, and realizes state synchronization for the first time under the output-coupled framework. A round-robin (RR) protocol is introduced to dynamically schedule the output-coupled communication among neurons to address the transmission efficiency bottleneck under limited bandwidth resources. To allocate communication resources more intelligently, a novel event-triggered (ET) mechanism is designed. Under this mechanism, the triggering threshold is constructed based on the last triggering instant and is updated according to the most current triggering instant. It significantly reduces overall resource consumption while ensuring control performance. Then, the joint Lyapunov function is constructed based on the designed observer-controller-protocol interaction dynamic model. It derived a quantitative relationship between the triggering frequency and the error decay boundary, thereby providing a quantifiable basis for precision tuning in network control. Finally, the effectiveness of the proposed method is verified by circuit simulation.