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Yayın Equilibrium and stability analysis of delayed neural networks under parameter uncertainties(Elsevier Science Inc, 2012-02-15) Faydasıçok, Özlem; Arik, SabriThis paper proposes new results for the existence, uniqueness and global asymptotic stability of the equilibrium point for neural networks with multiple time delays under parameter uncertainties. By using Lyapunov stability theorem and applying homeomorphism mapping theorem, new delay-independent stability criteria are obtained. The obtained results are in terms of network parameters of the neural system only and therefore they can be easily checked. We also present some illustrative numerical examples to demonstrate that our result are new and improve corresponding results derived in the previous literature.Yayın A new robust stability criterion for dynamical neural networks with multiple time delays(Elsevier Science BV, 2013-01-01) Faydasıçok, Özlem; Arik, SabriThis paper investigates the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with multiple time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we derive a new criterion for the robust stability of a class of delayed neural networks by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Different from those previously published conditions in the recent literature, the robust stability result presented in this paper not only establishes a time-independent relationship between the network parameters of the neural network, but also takes into account the number the neurons of the designed neural system. Some illustrative numerical examples are also given to make a detailed comparison between our result and the previously published corresponding results. This comparison proves that our result is new and can be considered an alternative condition to those of the previously reported robust stability results.Yayın A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks(Pergamon-Elsevier Science Ltd, 2013-08) Faydasıçok, Özlem; Arik, SabriThe main problem with the analysis of robust stability of neural networks is to find the upper bound norm for the intervalized interconnection matrices of neural networks. In the previous literature, the major three upper bound norms for the intervalized interconnection matrices have been reported and they have been successfully applied to derive new sufficient conditions for robust stability of delayed neural networks. One of the main contributions of this paper will be the derivation of a new upper bound for the norm of the intervalized interconnection matrices of neural networks. Then, by exploiting this new upper bound norm of interval matrices and using stability theory of Lyapunov functionals and the theory of homomorphic mapping, we will obtain new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete time delays under parameter uncertainties and with respect to continuous and slope-bounded activation functions. The results obtained in this paper will be shown to be new and they can be considered alternative results to previously published corresponding results. We also give some illustrative and comparative numerical examples to demonstrate the effectiveness and applicability of the proposed robust stability condition.Yayın Robust stability analysis of a class of neural networks with discrete time delays(Pergamon-Elsevier Science Ltd, 2012-05) Faydasıçok, Özlem; Arik, SabriThis paper studies the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of neural networks with discrete constant time delays under parameter uncertainties. The class of the neural network considered in this paper employs the activation functions which are assumed to be continuous and slope-bounded but not required to be bounded or differentiable. We conduct a stability analysis by exploiting the stability theory of Lyapunov functionals and the theory of Homomorphic mapping to derive some easily verifiable sufficient conditions for existence, uniqueness and global asymptotic stability of the equilibrium point. The conditions obtained mainly establish some time-independent relationships between the network parameters of the neural network. We make a detailed comparison between our results and the previously published corresponding results. This comparison proves that our results are new and improve and generalize the results derived in the past literature. We also give some illustrative numerical examples to show the effectiveness and applicability of our proposed stability results.
