Pinning Synchronization of Complex Switching Networks with a Leader of Nonzero Control Inputs

The evolution of the target system (leader) in pinning-controlled complex networks may need to be regulated by some control inputs for performing various practical tasks, e.g., obstacle avoidance, tracking highly maneuverable target, and so on. Motivated by this observation, we shall investigate the global pinning synchronization problems for complex switching networks for which the target system is subject to nonzero control inputs. First, using the idea of unit vector function method, a discontinuous coupling law is designed. With the aid of stability theory for switched systems, it is theoretically shown that synchronization in the network under this discontinuous coupling law can be achieved by choosing sufficiently large coupling strengths if the average dwell time (ADT) is bounded below by a positive constant. Second, we use the boundary layer method to design a continuous-coupling law. It has been theoretically shown that the synchronization error is ultimately uniformly bounded (UUB) under this continuous-coupling law. The chattering effect is also avoided in real implementation by using this continuous-coupling law. Furthermore, for networks with unknown external disturbances and unmodeled dynamics, neuro-adaptive-based coupling laws are designed to ensure that the synchronization error of the networks with undirected switching communication topologies under these laws is UUB. The obtained theoretical results are finally validated by performing numerical simulation on coupling Chua's circuit systems.