Prescribed-time synchronization for multiweighted complex networks: A switching control scheme

Abstract

This letter deals with an interesting intersection phenomenon of prescribed-time stability (PTSta) for dynamical systems, and develops a novel switching control scheme to investigate prescribed-time synchronization (PTSyn) for multiweighted and directly coupled complex networks. Different from most previous works that scholars only pay attention to designing the regulation function to ensure PTSta, we aim to select various parameters and uncover the mathematical mechanism of intersecting system state curves. We rigorously prove that, if the settling time is larger than 1, then no matter what the initial value is, the intersection exists only once before the settling time; otherwise, there is no intersection. Moreover, an energy consumption evaluation function is also put forward for PTSta, whose exact value is also calculated via exponential integrals. Then, this intersection theory is applied on the PTSyn of multiweighted complex networks, which is beneficial to construct the switching control scheme or choose the optimal parameters to reduce the energy cost. The rearranging variables’ order technique is utilized to conduct the multiweighted complex networks and obtain the synchronization criterion. Finally, four simulations are presented to verify theoretical results.