Practical fixed-time synchronization of fuzzy inertial neural networks with mixed time-varying delays: A parameterized solution approach

This paper addresses the unresolved problem of practical fixed-time synchronization (PFTS) with prescribed precision for fuzzy inertial neural networks (FINNs) subject to mixed time-varying delays (leakage, transmission, and distributed delays). Unlike existing studies that rely on Lyapunov–Krasovskii functionals, we propose a novel parameterized solution-based direct analysis approach, that eliminates variable substitution and reduces computational complexity. Key contributions include (1) first theoretical framework for PFTS in FINNs with leakage delays; (2) derivation of settling-time inequalities through scalar conditions; and (3) experimental validation showing faster convergence than prior methods. Numerical simulations demonstrate the efficacy under a precision threshold <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:mi mathvariant="bold-italic">ϵ</mml:mi> <mml:mo mathvariant="bold">=</mml:mo> <mml:mn mathvariant="bold">0</mml:mn> <mml:mo mathvariant="bold">.</mml:mo> <mml:mn mathvariant="bold">1</mml:mn> </mml:mrow> </mml:math> with convergence time <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mi mathvariant="bold-italic">T</mml:mi> </mml:mrow> <mml:mrow> <mml:mo mathvariant="bold">∗</mml:mo> </mml:mrow> </mml:msup> <mml:mo mathvariant="bold">≈</mml:mo> <mml:mn mathvariant="bold">7</mml:mn> <mml:mo mathvariant="bold">.</mml:mo> <mml:mn mathvariant="bold">6407</mml:mn> </mml:mrow> </mml:math> .