Consensus tracking control of discrete‐time second‐order agents over switching signed digraphs with arbitrary antagonistic relations

Abstract

SummaryThis article studies the problem of consensus tracking control for second‐order agents in multiagent systems over switching signed digraphs. Compared with the existing consensus tracking works on the structurally balanced signed digraph where the antagonistic relations exist only between two independent subgroups, this article explores a more general case for the first time, in the sense that the antagonistic relation is allowed between any two agents. On the basis of the design of a cooperation‐antagonism environment‐based distributed algorithm, suitable model transformation vectors are utilized to convert the stability of original system into a product convergence problem of time‐varying superstochastic matrices. By analyzing the convergence, algebraic conditions between positive and negative weights are established to ensure that all followers can eventually reach the leader's state under switching signed digraphs with arbitrary antagonistic relations. Simulation examples are provided to demonstrate the effectiveness of our results.