State Consensus for Discrete-time Multi-agent Systems over Time-varying Graphs

TL;DR

This paper introduces a new control protocol design approach based on the small gain theorem for achieving state consensus in discrete-time multi-agent systems over time-varying graphs, covering both stable and unstable cases.

Contribution

It proposes a novel small gain theorem-based method for designing consensus protocols for linear discrete-time multi-agent systems with time-varying connectivity.

Findings

Consensus achieved under weak uniform observability for stable systems

Consensus requires strong uniform observability for unstable systems

Numerical examples validate the theoretical results

Abstract

We study the state consensus problem for linear shift-invariant discrete-time homogeneous multi-agent systems (MASs) over time-varying graphs. A novel approach based on the small gain theorem is proposed to design the consensus control protocols for both neutrally stable and neutrally unstable MASs, assuming the uniformly connected graphs. It is shown that the state consensus can be achieved for neutrally stable MASs under a weak uniform observability condition; for neutrally unstable MASs, the state consensus entails a strong uniform observability condition. Two numerical examples are worked out to illustrate our consensus results.