Continuous-time double integrator consensus algorithms improved by an appropriate sampling *

This paper deals with the double integrator consensus problem. The objective is the design of a new consensus algorithm for continuous-time multi-agent systems. The dynamic of agents is assumed to be of double integrator type. The proposed algorithm considers that there are no sensors to measure the velocity of the agents. Thus the classical double integrator consensus algorithm leads to an oscillatory behavior if the communication graph is undirected and to instability if the graph is directed. The novel algorithm proposes to sampled, in an appropriate manner, part of the multi-agent systems state such that the algorithm converges. An expression of the consensus equilibrium is provided. Some examples are provided to show the efficiency of the new algorithm.