A new Lyapunov–Krasovskii functional for stability analysis of delayed neural network

This paper is concerned with new approaches to the stability analysis of delayed neural networks. By modifying the non-orthogonal polynomial-based integral inequality (NPII), a new delay-product functional (DPF) is formulated. On the basis of the proposed DPF, a Lyapunov–Krasovskii functional (LKF) is constructed where a new state introduced in the second-order Bessel–Legendre integral inequality (BLII) is included in augmented vectors of Lyapunov matrix. On account of this proposed LKF, the delay-dependent criterion is introduced in terms of linear matrix inequalities (LMIs) for stability analysis of neural networks time-varying delay. Two commonly used numerical examples are considered for demonstration purpose to test the efficacy of the proposed stability criterion.