STABILITY ANALYSIS OF QUATERNION-VALUED NEURAL NETWORKS WITH LEAKAGE DELAY AND ADDITIVE TIME-VARYING DELAYS

The paper proves global asymptotic stability for QVNNs with one leakage delay and two additive time‑varying delays via a tailored Lyapunov–Krasovskii functional that couples x(t) with the leakage integral, uses reciprocally convex bounds for additive delays, introduces free-weighting terms through a zero-identity, and aggregates the estimates into dV/dt ≤ η*Ωη with Ω < 0 implying stability. The candidate solution follows the same control-Lyapunov blueprint (LKF + reciprocally convex + Jensen/Wirtinger + Lipschitz slack variables + Ω < 0), but it proposes a somewhat different LKF and places the free-weighting matrices directly in V rather than as an added zero. Minor inaccuracies aside (e.g., stating V1 = x*P1x and then attributing a CP1C term to its derivative), the model’s reasoning reaches the same LMI condition and conclusion. Hence both are correct, but the constructions differ in details.