Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays

Chaouki Aouiti (1) , Patrick Coirault (2, 3) , Foued Miaadi (1) , Emmanuel Moulay (4)

1 Faculté des Sciences de Bizerte [Université de Carthage]
2 LIAS [Poitiers] - Laboratoire d'informatique et d'automatique pour les systèmes [EA 6315]
3 A&S - Automatique et Systèmes
4 XLIM-SRI - Systèmes et Réseaux Intelligents

This article deals with the finite time boundedness (FTB) and FTB-stabilization problem for a general class of neutral high-order Hopfield neural networks (NHOHNNs) with time delay in the leakage term and mixed time delays. The mixed time delays consist of both discrete time-varying delays and infinite distributed delays. By using the topological degree theory, sufficient conditions are established to prove the existence of equilibrium points. Then, the Lyapunov-Krasovskii functional (LKF) method is used to prove sufficient conditions for the FTB. These conditions are in the form of linear matrix inequalities (LMIs) and can be numerically checked. Furthermore, a state feedback control is constructed to solve the FTB-stabilization problem. Finally, some numerical examples are presented to show the effectiveness of our main results.

Mots clés: High-order neural networks; finite time boundedness; topological degree; stabilization; Lyapunov-Krasovskii functional; LMI; neutral systems; leakage delay

Domaines: Automatique / Robotique; Réseau de neurones [cs.NE]

Chaouki Aouiti, Patrick Coirault, Foued Miaadi, Emmanuel Moulay. Finite time boundedness of neutral high-order Hopfield neural networks with time delay in the leakage term and mixed time delays. Neurocomputing, 2017, 260, pp.378 - 392. ⟨10.1016/j.neucom.2017.04.048⟩. ⟨hal-01724031⟩