Non-reduced order method to global h-stability criteria for proportional delay high-order inertial neural networks

•The problem of global h stability for proportional delay HOINNs is investigated for the first time.•On the one hand, the h stability characterization generalizes the notions of uniform stability, exponential stability and asymptotically stability. On the other hand, h stability relaxes the concept of stability, including the case where the system trajectory converges to the neighborhood of the origin.•A new LKF contain ing a function h(t) is constructed.•The delay dependent global h stabil ity criteria of proportional delay HOINNs also apply to the proportional delay INNs. This article mainly explores the global h-stability for proportional delay high-order inertial neural networks. Without adopting reduced order method, a new Lyapunov–Krasovskii functional is constructed to derive the delay-dependent global h-stability criterion, which is new and improves some previous works. Moreover, the approach proposed in this article is also applicable to the global h-stability for multiple proportional delay high-order inertial neural networks. Finally, three examples and their numerical simulations are presented to illustrate the effectiveness of the method.