Resilient containment control of fractional-order multi-agent systems with uncertainty and time delay via non-fragile approaches

This paper investigated resilient containment control ( $\mathcal{C}\mathcal{C}$)-based consensus in fractional-order multi-agent systems ( $\mathcal{F}\mathcal{O}\mathcal{M}\mathcal{A}\mathcal{S}s$) subject to parametric uncertainties, communication time delays, and external disturbances. A non-fragile ( $\mathcal{N}\mathcal{F}$) distributed control protocol was proposed to accommodate controller perturbations and delay variations simultaneously. By integrating fractional calculus, algebraic graph theory, and an improved Razumikhin technique, we derived concise algebraic conditions ensuring all followers asymptotically converge to the convex hull that the leaders form under worst-case uncertainties. The results cover non-delayed and delayed cases and are expressed as simple, verifiable matrix inequalities. At the end, we provide examples to demonstrate the feasibility of the proposed method, including a numerical case study, and we illustrate the applicability of the developed theoretical results through designing a controller for electronic circuits.