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This chapter focuses on leader-follower consensus of nonlinear multi-agent systems in homogenous networks and heterogenous networks via distributed impulsive control, respectively. Leader-follower consensus problem in homogenous networks is studied in Sect. 2. Then in Sect. 3, a network-based leader-following consensus problem is considered, and distributed delayed impulsive protocols are designed for nonlinear multi-agent systems. Finally, bounded leader-follower consensus problem is well investigated in heterogenous networks in Sect. 4. How to obtain a tight error bound, to optimize the error bound, and to design the impulse intervals and coupling strength within a prescribed error bound are addressed.
The Laplacian eigenvalue spectrum of a complex network contains a great deal of information about the network topology and dynamics, particularly affecting the network synchronization process and performance. This article briefly reviews the recent progress in the studies of network synchronizability, regarding its spectral criteria and topological optimization, and explores the role of higher-order topologies in measuring the optimal synchronizability of large-scale complex networks.
