Delay-Dependent but \({\mathcal{N}}\)-Independent Pinning Synchronization Control for Switched Delayed Directed Networks
Hong Sang, Peng Wang, Ying Hong Zhao, Hong Shan Nie, Jun Hui Fu, Shuanghe Yu · SIAM Journal on Control and Optimization · 2025
Abstract. Lyapunov–Krasovskii functional (LKF) theory plays a significant role in formulating multifarious delay-dependent stability criteria for general systems with time delays. However, the existing delay-dependent results in the framework of LKF for delayed directed networks (DDNs) are generally dependent on the number [Formula: see text] of nodes in the networks, which are inapplicable to networks with a large size due to the computational complexity of exponential growth. For handling this situation, an interesting property of the Kronecker product is discovered and summarized in this work. Then, by constructing the topology-dependent multiple LKF approach and an ameliorative combined switching strategy, a delay-dependent but [Formula: see text]-independent pinning synchronization criterion is skillfully developed for the addressed switched delayed directed networks, where “[Formula: see text]-independent” indicates that the synchronization criterion is independent of the number [Formula: see text] of nodes. With the ameliorative combined switching strategy, different minimum dwell times are assured for each subnetwork, and none of the subnetworks are required to be synchronized in advance. Apart from that, a simple [Formula: see text]-independent pinning synchronization criterion for nonswitched DNNs is also discussed. Finally, the applicability of the proposed pinning synchronization approach is verified through a simulation example.