Non‐fragile control for consensus and attractiveness in fractional‐order multi‐agent systems with mixed time‐delays

Abstract

This paper presents a unified analytical framework for studying consensus and global attractiveness in Riemann–Liouville fractional‐order multi‐agent systems subject to mixed discrete and distributed time‐delays, structured parametric uncertainties, and non‐fragile control protocols. Both leader‐follower and leaderless network configurations are addressed within a single theoretical setting, where the coupling topology is modeled as a directed weighted graph. By constructing a suitable quadratic Lyapunov functional and systematically exploiting the composition properties of Riemann–Liouville fractional operators together with Young‐type matrix inequalities, delay‐dependent sufficient conditions for global attractiveness are established in a computationally tractable form. The consensus analysis is then extended to non‐fragile fractional‐order multi‐agent systems, yielding explicit algebraic criteria expressed as linear matrix inequalities, whose feasibility simultaneously guarantees consensus and provides the stabilizing feedback gain matrices. The derived conditions are further translated into spectral radius criteria, enabling efficient verification for large‐scale networks. Three numerical examples, covering the leader‐follower scenario, the leaderless scenario, and a global attractiveness test, are presented to validate the theoretical results and confirm the practical effectiveness of the proposed design methodology.