Robust cooperative synchronization of homogeneous agents with delays on directed communication graphs

TL;DR

This paper presents a less conservative LMI-based method for analyzing and designing delay-tolerant cooperative synchronization in homogeneous agents on directed graphs, decoupling agent dynamics from network topology.

Contribution

It introduces an extended synchronizing region concept with an LMI relaxation, enabling less conservative delay bounds and distributed control design without full topology knowledge.

Findings

Less conservative delay bounds for synchronization.

Decoupling agent dynamics from graph topology.

Validated approach with numerical example.

Abstract

This study deals with analysis and control of cooperative synchronization for identical agents interacting on a directed graph topology. The agents are considered to have general continuous linear time-invariant dynamics with homogeneous communication and/or control delays. An LMI approach based on a Lyapunov-Krasovskii functional is proposed, together with the synchronizing region concept, which decouples the single-agent dynamics from the detailed graph topology. Moreover, the conventional notion of synchronizing region is here extended by an LMI relaxation utilizing quasi-convex characteristic of the problem. This leads to less conservative results for the region of graph matrix eigenvalues in the complex domain, where the synchronization is guaranteed. The proposed method to calculate the allowable delay bound for synchronization is also less conservative as compared to the results from the literature. Furthermore, two designs for distributed state-feedback control are suggested. The precise delay value and the detailed graph topology need not be known for their application; it suffices only to know the upper bound on the delay and the approximate region where the Laplacian eigenvalues lie. Specific improvements over the results existing in the literature are demonstrated by a numerical example, which validates the proposed approaches.