Dynamic leader-following consensus for asynchronous sampled-data multi-agent systems under switching topology

Abstract

This paper investigates the leader-following consensus problem for asynchronous sampled-data multi-agent systems with an active leader and under switching topology, in which the asynchrony means that each agent’s update actions are independent of the others’. First, the dynamic leader-following consensus problem for asynchronous sampled-data systems is transformed into the convergence problem of products of infinite general sub-stochastic matrices (PIGSSM), where the general sub-stochastic matrices are matrices with row sum no more than 1 but their elements are not necessarily nonnegative. We develop a method to cope with the corresponding convergence problem by matrix decomposition. In particular, we split the general sub-stochastic matrix into a sub-stochastic matrix which is a nonnegative matrix with row sum no more than 1, and a matrix with negative elements and row sum 0. Then based on a graphical approach and matrix analysis technique, we present a sufficient condition for the achievement of dynamic leader-following consensus in the asynchronous setting. Finally, simulation examples are demonstrated to verify the theoretical results.