Synchronization on complex dynamical networks via intermittently sampled-data pinning control

Each specific control strategy has a unique advantage, and combining multiple control strategies can harness the advantages of these strategies. Designing new control strategies by integrating different control strategies is an interesting and challenging topic. This paper introduces an intermittently sampled-data pinning (ISP) control strategy, which merges intermittent control, sampled-data control and pinning control, to study synchronization on complex dynamical networks. The ISP control strategy is proposed to solve three difficulties: first, the controllers transmitting feedback signals may be discontinuous; second, the controllers often cannot operate continuously in practical applications; third, it is usually hard to control all nodes in a dynamical network as the network size is huge. Sufficient conditions are obtained for realizing synchronization on dynamical networks. Furthermore, time delays are incorporated into the proposed control strategy to address the untimely reception of feedback signals and achieve the synchronization conditions on dynamical networks. Finally, two numerical examples demonstrate the effectiveness of the proposed control method.