Sabri Arik

Neural networks letter: Robust stability analysis of a class of neural networks with discrete time delays

This 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.

An improved robust stability result for uncertain neural networks with multiple time delays.

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.

Equilibrium and stability analysis of delayed neural networks under parameter uncertainties

Abstract 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.

New Criteria for Global Robust Stability of Delayed Neural Networks With Norm-Bounded Uncertainties

In this paper, we study the global asymptotic robust stability of delayed neural networks with norm-bounded uncertainties. By employing the Lyapunov stability theory and homeomorphic mapping theorem, we derive some new types of sufficient conditions ensuring 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. An important aspect of our results is their low computational complexity, as the reported results can be verified by checking some properties of symmetric matrices associated with the uncertainty sets of the network parameters. The obtained results are shown to be generalizations of some of the previously published corresponding results. Some comparative numerical examples are also constructed to compare our results with some closely related existing literature results.

A new upper bound for the norm of interval matrices with application to robust stability analysis of delayed neural networks

The 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.

Further analysis of global robust stability of neural networks with multiple time delays

Abstract 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.

A new robust stability criterion for dynamical neural networks with multiple time delays

This 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.

New robust stability results for bidirectional associative memory neural networks with multiple time delays

In this paper, the robust stability problem is investigated for a class of bidirectional associative memory (BAM) neural networks with multiple time delays. By employing suitable Lyapunov functionals and using the upper bound norm for the interconnection matrices of the neural network system, some novel sufficient conditions ensuring the existence, uniqueness and global robust stability of the equilibrium point are derived. The obtained results impose constraint conditions on the system parameters of neural network independent of the delay parameters. Some numerical examples and simulation results are given to demonstrate the applicability and effectiveness of our results, and to compare the results with previous robust stability results derived in the literature.

A new condition for robust stability of uncertain neural networks with time delays

This paper is concerned with the global asymptotic stability problem of dynamical neural networks with multiple time delays under parameter uncertainties. First carrying out an analysis of existence and uniqueness of the equilibrium point by means of the Homeomorphism theory, and then, studying the global asymptotic stability of the equilibrium point by constructing a suitable Lyapunov functional, we derive a new global robust stability criterion for the class of delayed neural networks with respect to the Lipschitz activation functions. The result obtained establishes a relationship between the neural network parameters only and it is independent of the time delay parameters. It is shown that the established stability condition generalizes some existing ones and it can be considered to an alternative result to some other corresponding results derived in previous literature. We also give some comparative numerical examples to demonstrate the validity and effectiveness of our proposed result.

New global robust stability condition for uncertain neural networks with time delays

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.