Mean-square H_∞ antagonistic formations of second-order multi-agent systems with multiplicative noises and external...

In physical systems, since the acceleration is always regard as the control input, it is meaningful to study the coordination problems of the second-order multi-agent system. This paper devotes to the mean-square H_∞ antagonistic formation control of second-order multi-agent systems with multiplicative noises and external disturbances under directed signed topologies. To force all agents achieve antagonistic formation and attenuate the effect of communication noises and external disturbances, a novel distributed consensus control protocol with a time-invariant control gain is proposed where only the information that received from neighbors is utilized. And then, by combining the theories of graph, robust H_∞ control and stochastic analysis, some matrix inequalities conditions are deduced. It is proved that under the designed control protocol, the state of each agent converge to its own desired formation in its allied groups in the sense of mean square. Furthermore, numerical simulations are given for the purpose of showing that the proposed theoretical results are effective.