Robust output consensus of homogeneous multi-agent systems with negative imaginary dynamics

Abstract

This paper addresses the robust output consensus problem for multiple homogeneous negative imaginary (NI) systems subject to L2 external disturbances and model uncertainties. The principal aim of this paper is to extend and overcome limitations in previous studies which had required restrictive assumptions to be imposed and thereby derive necessary and sufficient conditions for robust output consensus of networked NI systems when such assumptions do not hold. In doing so, the recently published robust NI stability results are utilised. An advantage of the derived conditions is that they depend on the dc and infinite frequency gains of the systems as well as the network graph but not on the precise dynamics of the systems. Furthermore, it is shown that the derived conditions specialise to the earlier results in literature either by imposing the same assumptions or by imposing different ones which had not been known previously. It is also shown that the derived conditions simplify in the single-input single-output case and an intuition about these results is provided. Finally, examples are given which demonstrate the effectiveness of the proposed results over earlier results when earlier assumptions are not met.