Quanjun Wu

Global exponential stability of impulsive differential equations with any time delays

Abstract The main objective of this letter is to further investigate the global exponential stability of a class of general impulsive retarded functional differential equations. Several new criteria on global exponential stability are analytically established based on Lyapunov function methods combined with Razumikhin techniques. The obtained results extend and generalize some results existing in the literature. An example, along with computer simulations, is included to illustrate the results.

Average Consensus in Delayed Networks of Dynamic Agents with Impulsive Effects

In this paper, the issues of average consensus in undirected delayed networks of dynamic agents with impulsive effects are investigated. The primary contribution of this paper is to propose the consensus schemes in undirected delayed networks of dynamic agents having impulsive effects as well as fixed, switching topology. Based on impulsive stability theory on delayed dynamical systems, we derive some simple sufficient conditions under which all the nodes in the network achieve average consensus globally exponentially. It is shown that average consensus in the networks is heavily dependent on impulsive effects of communication topology of the networks. Subsequently, two numerical examples illustrate and visualize the effectiveness and feasibility of our theoretical results.

Pinning impulsive synchronization in coupled delayed directed dynamical networks

In this brief, the issues of pinning synchronization in a coupled delayed directed dynamical network are investigated via impulsive control, and a simple yet generic criterion of pinning impulsive synchronization for such coupled network is derived analytically. It is shown that a single impulsive controller can always pin a given coupled delayed directed network to a desired homogenous solution. Subsequently, the theoretic results are illustrated by a typical small-world (SW) network composing of the well known Hodgkin-Huxley neuron oscillators. Numerical simulations are finally given to demonstrate the effectiveness of the proposed control methodology.

Impulsive consensus for second-order multi-agent systems with a reference velocity and input delays

In this brief, a distributed impulsive algorithm for second-order multi-agent systems with a group reference velocity and input time delays is proposed. A distinctive feature of the algorithm is to address second-order consensus problems with local instantaneous interaction, where each agent can only exchange the information with its neighbors at a series of discrete-time instants and follow a desired reference velocity in the meantime. Some generic criteria for such algorithm over, respectively, directed fixed and switching network topologies are derived analytically. It is shown that consensus can be asymptotically reached if the interaction graph of the system has a spanning tree and the input time delays are less than the interaction intervals, which is assumed to be less than a given threshold value. Subsequently, numerical simulations are given to illustrate and visualize the effectiveness and feasibility of the theoretical results.

Impulsive consensus seeking in delayed networks of multi-agents

This present paper addresses impulsive consensus problem in directed networks of dynamic agents having communication delays Based on impulsive control theory on delayed dynamical systems, a simple impulsive consensus protocol for such networks is proposed, and a generic criterion for solving average consensus problem is analytically derived It is shown that global average consensus of a directed delayed networked multi-agent systems can be achieved by a suitable design of the impulsive gain and impulsive interval Simulations are presented that are consistent with the theoretical results.