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We discuss a new consensus problem -a group consensus problem -in networks of dynamic agents. For a complex network consisting of several sub-networks owing to physical quantities or task distributions, it is concerned with this case that the agents in a sub-network share a consistent value while there is no agreement between any two sub-networks. When the information exchange is directed, a novel consensus protocol is designed to solve the group consensus problem. The convergence analysis is discussed and several criteria are established based on graph theories and matrix theories. Simulation results are presented to demonstrate the effectiveness of the theoretical results.

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SUMMARYStabilization problems of networked control systems (NCSs) with bounded packet losses and transmission delays are addressed. We model such NCSs as a class of switched systems, and establish stabilizing conditions in the form of matrix inequalities by using packet-loss dependent Lyapunov functions. By solving the inequalities, packet-loss dependent controllers are designed for two types of packet-loss processes: one is an arbitrary packet-loss process, and the other is a Markovian packet-loss process. Several numerical examples and simulations are worked out to demonstrate the effectiveness of the proposed design techniques.