Strict‐LMI Criteria for Mittag–Leffler Stability With H∞ Performance in Nonlinear Large‐Scale Singular Fractional‐Order Systems

ABSTRACT This paper presents a novel and unified framework for analyzing Mittag–Leffler stability with guaranteed performance in a broad class of nonlinear large‐scale singular fractional‐order systems (LSFOSS). Existing studies have predominantly addressed finite‐time or asymptotic stability, often neglecting the intrinsic power‐law decay of fractional dynamics and the simultaneous enforcement of disturbance attenuation in the sense. The analysis of such systems is particularly challenging due to the coexistence of singular algebraic constraints, fractional‐order dynamics with power‐law decay, nonlinear large‐scale interconnections, and external disturbances. To bridge this gap, we construct Lyapunov functionals specifically designed for singular fractional‐order structures and nonlinear interconnections, capturing both the long‐memory characteristics and the algebraic constraints inherent to LSFOSS. By imposing quadratic constraints on nonlinear perturbations, we derive new, tractable, and strict linear matrix inequality (LMI) criteria that ensure Mittag–Leffler stability together with performance. A variable‐substitution transformation is proposed to convert non‐strict feasibility conditions into strict LMIs, significantly enhancing computational tractability while avoiding conservatism. To the best of our knowledge, this work provides a first systematic LMI‐based framework that integrates Mittag–Leffler stability with guaranteed performance for nonlinear LSFOSS. The applicability and effectiveness of the proposed method are illustrated through large‐scale singular fractional‐order neural network models with ring and hub topologies, supported by comprehensive numerical simulations.