Robust Stability Of Neural Networks Research Articles

A new delay-independent condition for global robust stability of neural networks with time delays

This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results.

Analysis of Time-Delayed Neural Networks via Rightmost Eigenvalue Positions

Neural networks have been frequently used in various areas. In the implementation of the networks, time delays and uncertainty are present and known to lead to complex behaviors, which are hard to predict using classical analysis methods. In this study, stability and robust stability of neural networks considering time delays and parametric uncertainty is studied. For stability analysis, the rightmost eigenvalues (or dominant characteristic roots) are obtained by using an approach based on the Lambert W function. The Lambert W function has already been embedded in various commercial software packages (e.g., MATLAB, Maple and Mathematica). In a way similar to non-delayed systems, stability is determined from the positions of the characteristic roots in the complex plane. Conditions for oscillation and robust stability are also given. Numerical examples are provided and the results are compared to existing approaches (e.g., bifurcation method) and discussed.

An analysis of stability of uncertain neural networks with multiple time delays

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.

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

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.

Delay-Dependent Robust Stability of Cellular Neural Networks with Time-Varying Discrete and Distributed Delay

Delay-dependent robust stability of neural networks with discrete and distributed delays is considered in this paper. Stability criteria are derived in LMIs avoiding bounding certain cross terms and the restriction of derivative of time-varying delay is removed. Numerical examples are given to indicate significant improvements over some existing results.

Delay-dependent global robust stability criterion for neural networks with neutral-type time-varying delays

The problem of global robust stability for neural networks with neutral-type time-varying delays is investigated in this paper. Neutral differential equations are used to construct this class of neural networks. The time-varying delay function is bounded, and it is not required to be continuously differentiable. A new delay-dependent global stability criterion is derived based on the Lyapunov-Krasovskii functional approach. The criterion is formulated in terms of a linear matrix inequality. Numerical examples are given to illustrate the validity of the proposed stability criterion.

Global Asymptotic Robust Stability and Global Exponential Robust Stability of Neural Networks with Time-Varying Delays

In this paper, based on nonnegative matrix theory, the Halanay's inequality and Lyapunov functional, some novel sufficient conditions for global asymptotic robust stability and global exponential robust stability of neural networks with time-varying delays are presented. It is shown that our results improve and generalize several previous results derived in the literatures. From the obtained results, some linear matrix inequality criteria are derived. Finally, a simulation is given to show the effectiveness of the results.

A new result on global exponential robust stability of neural networks with time-varying delays

In this paper, the global exponential robust stability of neural networks with time-varying delays is investigated. By using nonnegative matrix theory and the Halanay inequality, a new sufficient condition for global exponential robust stability is presented. It is shown that the obtained result is different from or improves some existing ones reported in the literatures. Finally, some numerical examples and a simulation are given to show the effectiveness of the obtained result.

Delay-dependent robust stability criteria for delay neural networks with linear fractional uncertainties

This article investigates the problem of robust stability for neural networks with time-varying delays and parameter uncertainties of linear fractional form. By introducing a new Lyapunov-Krasovskii functional and a tighter inequality, delay-dependent stability criteria are established in term of linear matrix inequalities (LMIs). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

Robust stability of discrete-time LPD neural networks with time-varying delay

This paper presents a new approach to the robust stability of discrete-time LPD neural networks with time-varying delay and with normed bounded uncertainties as well as polytopic type uncertainties. Based on Lyapunov stability theory and the S-procedure, we derive robust stability criteria in terms of linear matrix inequalities (LMI) which are solvable by several available algorithms. We show that some of the existing results on robust stability of neural networks are corollaries of main results of this paper. Numerical examples are given to illustrate the effectiveness of our theoretical results.

Global robust stability of neural networks with multiple discrete delays and distributed delays

The problem of global robust stability is investigated for a class of uncertain neural networks with both multiple discrete time-varying delays and distributed time-varying delays. The uncertainties are assumed to be of norm-bounded form and the activation functions are supposed to be bounded and globally Lipschitz continuous. Based on the Lyapunov stability theory and linear matrix inequality technique, some robust stability conditions guaranteeing the global robust convergence of the equilibrium point are derived. The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. Two examples are given to show the effectiveness of the proposed results.

Robust stability for neural networks with time-varying delays and linear fractional uncertainties

The problem of robust stability for neural networks with time-varying delays and parameter uncertainties is investigated in this paper. The parameter uncertainties are described to be of linear fractional form, which include the norm bounded uncertainties as a special case. By introducing a new Lyapunov–Krasovskii functional and considering the additional useful terms when estimating the upper bound of the derivative of Lyapunov functional, new delay-dependent stability criteria are established in term of linear matrix inequality (LMI). It is shown that the obtained criteria can provide less conservative results than some existing ones. Numerical examples are given to demonstrate the applicability of the proposed approach.

Robust exponential stability analysis of neural networks with multiple time delays

This paper considers the robust stability of neural networks with multiple delays. Based on Lyapunov stability theory and linear matrix inequality technique, some new delay independent conditions are derived to guarantee the global robust exponential stability of the equilibrium point. Furthermore, the obtained results are generalized to the interval neural networks and bidirectional associative memory (BAM) neural networks. Two examples are used to show the effectiveness of the obtained results.

Global robust stability of neural networks with time varying delays

In this paper, we study the global robust stability of neural networks with time varying delays using the Lyapunov functional method and matrix inequality technique. Several sufficient conditions are presented to show the existence of equilibrium and global robust stability of neural networks, which is easy to apply. Then we give a simulation to justify the obtained results.

New necessary and sufficient conditions for absolute stability of neural networks

This paper presents new necessary and sufficient conditions for absolute stability of asymmetric neural networks. The main result is based on a solvable Lie algebra condition, which generalizes existing results for symmetric and normal neural networks. An exponential convergence estimate of the neural networks is also obtained. Further, it is demonstrated how to generate larger sets of weight matrices for absolute stability of the neural networks from known normal weight matrices through simple procedures. The approach is nontrivial in the sense that non-normal matrices can possibly be contained in the resulting weight matrix set. And the results also provide finite checking for robust stability of neural networks in the presence of parameter uncertainties.

An analysis of global robust stability of neural networks with discrete time delays

This Letter presents a new sufficient condition for the existence, uniqueness and global robust asymptotic stability of the equilibrium point for neural networks with discrete time delays. The obtained condition can be easily verified as it is in terms of the network parameters only. Some numerical examples are given to compare our results with previous robust stability results derived in the literature.

Global robust stability for neural networks with delays

The problem of global robust stability of neural networks with time delays and uncertainties is investigated. The uncertainties are assumed to be norm-bounded. The problem is discussed based on the Lyapunov method and linear matrix inequality (LMI) techniques. A novel criterion is given to ascertain the robust stability of the system. The criterion is expressed in terms of LMIs. It is computationally efficient, since the LMIs can be easily solvable by various convex optimization algorithms.

LMI-based robust stability analysis of neural networks with time-varying delay

The robust stability of neural networks with time-varying delay and parametric uncertainties is considered here. The stability condition is given in terms of a linear matrix inequality (LMI). Numerical example is given to demonstrate the effectiveness of our theoretical results.

A note on the robust stability of neural networks with time delay

Abstract The robust stability of neural networks with time-varying delay and time-varying parametric uncertainties is considered. The stability condition is given in terms of linear matrix inequality (LMI). Numerical example is presented to demonstrate the effectiveness of our theoretical results.