Robust consensus of multi-agent systems with uncertain communication topology

Distributed robust consensus problem for a class of multi-agent systems (MASs) with uncertain communication topology is investigated. We propose a state linear transformation by constructing the incidence matrix of a directed spanning tree in the nominal communication topology, and transform the problem of state consensus of uncertain multiagent systems into the problem of robust partial asymptotic stability of corresponding linear systems. Firstly, we use the linear transformation constructed from a directed spanning tree to transform the closed uncertain MAS into a reduced-order system. Secondly, by using decomposition of perturbation Laplacian matrix, we design a quadratic stabilization robust controller for the reduced-order system, and derive a sufficient condition guaranteeing all agents's states to achieve asymptotic consensus. Based on the condition, the design problem of protocol parameters is converted into finding the feasible solution of linear matrix inequalities. Finally, the effectiveness and feasibility of the proposed approach is verified by simulation examples. © 2020, Editorial Department of Control Theory & Applications South China University of Technology. All right reserved.