Consecutive and Periodic Intermittent Cluster Synchronization of Positive Complex Networks

This paper aims to address the problem of observer based cluster synchronization control in positive complex networks. First, a novel cluster-based positive synchronization control framework is established for complex networks with isolated nodes, which has lower computational and communication burdens than existing frameworks. Subsequently, two types of controllers are designed, observer-based consecutive controllers and periodic intermittent controllers, where the latter can reduce unnecessary information transmission and control costs. Concurrently, the observer design exhibits enhanced flexibility. The positivity and stability of the complex networks are rigorously guaranteed by employing piecewise copositive Lyapunov functions and linear programming approach. On the basis of the above design, the complex networks can reachan prescribed performance in a limited working time. Finally, two examples are provided to justify the validity and superiority of the presented approach.