Robust Consensus Analysis and Design under Relative State Constraints or Uncertainties

TL;DR

This paper develops a new method for analyzing and designing distributed robust consensus controllers for multi-agent systems with relative-state constraints or uncertainties, using system transformation and LMI-based conditions.

Contribution

It introduces a novel approach that transforms the problem into a network of Lur'e systems and derives distributed LMI conditions for robust consensus design.

Findings

The proposed method effectively achieves robust consensus under constraints.

The approach is validated through numerical examples.

Theoretical conditions ensure stability and robustness.

Abstract

This paper proposes a new approach to analyze and design distributed robust consensus control protocols for general linear leaderless multi-agent systems (MASs) in presence of relative-state constraints or uncertainties. First, we show that the MAS robust consensus under relative-state constraints or uncertainties is equivalent to the robust stability under state constraints or uncertainties of a transformed MAS. Next, the transformed MAS under state constraints or uncertainties is reformulated as a network of Lur'e systems. By employing S-procedure, Lyapunov theory, and Lasalle's invariance principle, a sufficient condition for robust consensus and the design of robust consensus controller gain are derived from solutions of a distributed LMI convex problem. Finally, numerical examples are introduced to illustrate the effectiveness of the proposed theoretical approach.