Leader-following consensus of linear multi-agent systems with strict negative imaginary uncertainties

This paper considers the leader-following consensus problem of linear multi-agent systems with strict negative imaginary (SNI) uncertainties. It is assumed that the followers have homogeneous nominal dynamics while subject to different model uncertainties with SNI property, leading to weakly heterogeneous multi-agent systems. In the case of undirected topology, the control protocol is designed for multi-agent systems based on the relative states of neighbouring followers and the leader. It is shown that the control protocol can achieve leader-following state consensus for networked systems that followers have SNI uncertainties. A necessary and sufficient condition for the nominal networked system to be negative imaginary (NI) and satisfying gain condition is presented by decoupling the feedback controller from communication topology. Furthermore, a sufficient condition in terms of linear matrix inequalities (LMI) is derived for the leader-following consensus controller. Simulation example is provided to validate the effectiveness of the results.