Relaxed Stability Criteria for Delayed Memristor-Based Neural Network Systems via a Novel Matrix-Separation Legendre Inequality

This article studies the issue of stability in memristor-based neural network (MNN) systems with time-varying delays. First, a novel matrix-separation Legendre inequality is proposed to achieve a tight hierarchical bound on augmented-type integral terms. To derive implementable inequality conditions, several delay-dependent matrices are introduced to eliminate the reciprocal terms associated with time-varying delay. Furthermore, a new Lyapunov–Krasovskii (L–K) functional is proposed by incorporating augmented-type double integrals and delay-product terms. A series of free-weighting matrices are introduced into the L–K functional, leveraging the zero-sum equations and the S-procedure pertaining to both the delay and its derivative. Based on the proposed matrix-separation Legendre inequality and L–K functional, the derived stability conditions exhibit reduced conservatism, as validated by three numerical cases and simulation results.