Leader-based Multi-agent Consensus: Robust Control Design and Stability Analysis

In this paper, the robust absolute stability property of multi-agent systems by transforming the original system into a Lur’e system is presented. Different configurations of multi-agent systems are considered, which they include parametric uncertainty. These systems are primarily stabilized by applying robust design techniques to further verify the absolute stability property of the closed loop system, taking into account the parametric uncertainty. To solve the problem of robust absolute stability, the strict positive realness property (SPR) of a fictitious transfer function needs to be verified. Sufficient conditions to verify the robust absolute stability property of leader-based multi-agent systems with parametric uncertainty using a sign decomposition technique that guarantees the positivity of multivariable polynomials are presented. Therefore, the aim of this work is to present a method to analyze the robust absolute stability of uncertain leader-based multi-agent systems.