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2012 - 20146
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Yazar: Arik, Sabri × Konu: Criteria ×

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Listeleniyor 1 - 6 / 6
  • Küçük Resim
    Yayın
    Equilibrium and stability analysis of delayed neural networks under parameter uncertainties
    (Elsevier Science Inc, 2012-02-15) Faydasıçok, Özlem; Arik, Sabri
    This 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.
  • Küçük Resim
    Yayın
    Further analysis of global robust stability of neural networks with multiple time delays
    (Pergamon-Elsevier Science Ltd, 2012-04) Faydasıçok, Özlem; Arik, Sabri
    This paper deals with the problem of the global robust asymptotic stability of the class of dynamical neural networks with multiple time delays. We propose a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point under parameter uncertainties of the neural system. We first prove the existence and uniqueness of the equilibrium point by using the Homomorphic mapping theorem. Then, by employing a new Lyapunov functional, the Lyapunov stability theorem is used to establish the sufficient condition for the asymptotic stability of the equilibrium point. The obtained condition is independent of time delays and relies on the network parameters of the neural system only. Therefore, the equilibrium and stability properties of the delayed neural network can be easily checked. We also make a detailed comparison between our result and the previous corresponding results derived in the previous literature. This comparison proves that our result is new and improves some of the previously reported robust stability results. Some illustrative numerical examples are given to show the applicability and advantages of our result.
  • Küçük Resim
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    Further analysis of stability of uncertain neural networks with multiple time delays
    (Springer International Publishing AG, 2014-01-27) Arik, Sabri
    This paper studies the robust stability of uncertain neural networks with multiple time delays with respect to the class of nondecreasing activation functions. By using the Lyapunov functional and homeomorphism mapping theorems, we derive a new delay-independent sufficient condition the existence, uniqueness, and global asymptotic stability of the equilibrium point for delayed neural networks with uncertain network parameters. The condition obtained for the robust stability establishes a matrix-norm relationship between the network parameters of the neural system, and therefore it can easily be verified. We also present some constructive numerical examples to compare the proposed result with results in the previously published corresponding literature. These comparative examples show that our new condition can be considered as an alternative result to the previous corresponding literature results as it defines a new set of network parameters ensuring the robust stability of delayed neural networks.
  • Küçük Resim
    Yayın
    An analysis of stability of uncertain neural networks with multiple time delays
    (Pergamon-Elsevier Science Ltd, 2013-09) Faydasıçok, Özlem; Arik, Sabri
    This paper deals with the problem of robust stability of neural networks with multiple time delays with the class of unbounded and nondecreasing activation functions. By constructing a suitable Lyapunov functional and applying the homeomorphism mapping theorem, we derive new delay-independent sufficient conditions that establish the existence, uniqueness and global asymptotic stability of the equilibrium point for the delayed neural networks under norm-bounded uncertain network parameters. The conditions obtained for robust stability are expressed in terms of network parameters only, therefore they can be easily checked. An advantage of the proposed results is that they consider the number of the neurons in the stability conditions. We also give some numerical examples with comparative results to demonstrate the applicability of our stability conditions. These comparative examples will also show the advantages of the obtained results over the corresponding robust stability results derived in the previous literature.
  • Küçük Resim
    Yayın
    New global robust stability condition for uncertain neural networks with time delays
    (Elsevier Science BV, 2014-10-22) Özcan, Neyir; Arik, Sabri
    In this paper, we investigate the robust stability problem for the class of delayed neural networks under parameter uncertainties and with respect to nondecreasing activation functions. Firstly, some new upper bound values for the elements of the intervalized connection matrices are obtained. Then, a new sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for this class of neural networks is derived by constructing an appropriate Lyapunov-Krasovskii functional and employing homeomorphism mapping theorem. The obtained result establishes a new relationship between the network parameters of the neural system and it is independent of the delay parameters. A comparative numerical example is also given to show the effectiveness, advantages and less conservatism of the proposed result.
  • Küçük Resim
    Yayın
    An improved robust stability result for uncertain neural networks with multiple time delays
    (Pergamon-Elsevier Science Ltd, 2014-06) Arik, Sabri
    This paper proposes a new alternative sufficient condition for the existence, uniqueness and global asymptotic stability of the equilibrium point for the class of delayed neural networks under the parameter uncertainties of the neural system. The existence and uniqueness of the equilibrium point is proved by using the Homomorphic mapping theorem. The asymptotic stability of the equilibrium point is established by employing the Lyapunov stability theorems. The obtained robust stability condition establishes a new relationship between the network parameters of the system. We compare our stability result with the previous corresponding robust stability results derived in the past literature. Some comparative numerical examples together with some simulation results are also given to show the applicability and advantages of our result.