This paper investigates synchronization issues of a heterogeneous complex network with a general switching topology in the sense of boundedness, when no complete synchronization manifold exists. Several sufficient conditions are established with the Lyapunov method and the differential analysis of convergence to determine the existence and estimate the convergence domain for the local and global bounded synchronization of a heterogeneous complex network. By using the consensus convergence of a switched linear system associated with the switching topology, explicit bounds of the maximum deviation between nodes are obtained in the form of a scalar inequality involving the property of the consensus convergence, the homogeneous and heterogeneous dynamics of individual nodes for the local and global cases. These analytical results are simple yet generic, which can be used to explore synchronization issues of various complex networks. Finally, a numerical simulation illustrates their effectiveness.postprin

This paper investigates the local consensus issue for multiagent systems with nonlinear dynamics and time-varying delays. By defining a weighted average state of the agents and applying local linearization, we show that the local consensus of the agents in a directed communication network can be guaranteed by the asymptotic stability of several decoupled delayed systems. Then, by employing a novel Lyapunov-Krasovskii functional, proposing a new extended reciprocally convex approach and using some matrix analysis, we derive a sufficient condition for the local consensus in terms of linear matrix inequalities associated with the dynamics of the agents, the eigenvalues of Laplacian matrix, and the time-varying delay. Finally, two numerical examples are provided to show the effectiveness of the analytical results.