Second-order consensus for directed multi-agent systems with sampled data

This paper deals with the consensus problem of second-order multi-agent systems with sampled data. Because of the unavailable velocity information, consensus problem is studied only by using the sampled position information. The final consensus states of multi-agent system are given. And a necessary and sufficient consensus condition is provided, which depends on the parameters of sampling interval, eigenvalues of Laplacian matrix, and coupling strengths. Then, the case that both the sampled position and velocity information can be obtained is discussed. On the basis of introducing a time-varying piecewise-continuous delay and proposing a novel time-dependent Lyapunov functional, the sufficient consensus condition is presented, and the upper bound of sampling interval can be estimated. Simulation examples are provided finally to demonstrate the effectiveness of the proposed design methods. Copyright (c) 2013 John Wiley & Sons, Ltd.