Asymptotic stability analysis in uncertain multi-delayed state neural networks via Lyapunov-Krasovskii theory

Authors:
Fernando O. Souza;Reinaldo M. Palhares;Petr Ya. Ekel
Affiliations:
Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos, 6627 - 31270-010, Belo Horizonte, MG, Brazil;Department of Electronics Engineering, Federal University of Minas Gerais, Av. Antônio Carlos, 6627 - 31270-010, Belo Horizonte, MG, Brazil;Graduate Program in Electrical Engineering, Pontifical Catholic University of Minas Gerais, Av. Dom José Gaspar, 500 - 30535-610, Belo Horizonte, MG, Brazil
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2007

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Abstract

This paper presents a new approach to the analysis of asymptotic stability of artificial neural networks (ANN) with multiple time-varying delays subject to polytope-bounded uncertainties. This approach is based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique with the use of a recent Leibniz-Newton model based transformation without including any additional dynamics. Three examples with numerical simulations are used to illustrate the effectiveness of the proposed method. The first example considers the neural network with multiple time-varying delays, which may be seen as a particular case of the second example where it is subject to uncertainties and multiple time-varying delays. Finally, the third example analyzes the stability of the neural network with higher numbers of neurons subject to a single time-delay. The Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability in the bifurcation point.