title: Enhancing speed of pinning synchronizability: low-degree nodes with high feedback gains.
abstract: Controlling complex networks is of paramount importance in science and engineering. Despite recent efforts to improve controllability and synchronous strength, little attention has been paid to the speed of pinning synchronizability (rate of convergence in pinning control) and the corresponding pinning node selection. To address this issue, we propose a hypothesis to restrict the control cost, then build a linear matrix inequality related to the speed of pinning controllability. By solving the inequality, we obtain both the speed of pinning controllability and optimal control strength (feedback gains in pinning control) for all nodes. Interestingly, some low-degree nodes are able to achieve large feedback gains, which suggests that they have high influence on controlling system. In addition, when choosing nodes with high feedback gains as pinning nodes, the controlling speed of real systems is remarkably enhanced compared to that of traditional large-degree and large-betweenness selections. Thus, the proposed approach provides a novel way to investigate the speed of pinning controllability and can evoke other effective heuristic pinning node selections for large-scale systems.
authors.affiliation: Guangdong Province Key Laboratory of Popular High Performance Computers, College of Computer Science and Software Engineering, Shenzhen University, Nanhai Avenue 3688, Shenzhen 518060, P. R. China.|Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230027, P. R. China.|Physics Department, University of Fribourg, Chemin du Musée 3, 1700 Fribourg Switzerland.
authors.forename: Ming-Yang
authors.initials: MY
authors.lastname: Zhou
authors.affiliation: Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230027, P. R. China.
authors.forename: Zhao
authors.initials: Z
authors.lastname: Zhuo
authors.affiliation: Guangdong Province Key Laboratory of Popular High Performance Computers, College of Computer Science and Software Engineering, Shenzhen University, Nanhai Avenue 3688, Shenzhen 518060, P. R. China.|Physics Department, University of Fribourg, Chemin du Musée 3, 1700 Fribourg Switzerland.
authors.forename: Hao
authors.initials: H
authors.lastname: Liao
authors.affiliation: Department of Electronic Science and Technology, University of Science and Technology of China, Hefei 230027, P. R. China.
authors.forename: Zhong-Qian
authors.initials: ZQ
authors.lastname: Fu
authors.affiliation: Web Sciences Center, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 611731, P. R. China.
authors.forename: Shi-Min
authors.initials: SM
authors.lastname: Cai