Global Robust Stability Analysis Research Articles

Novel results on global stability analysis for multiple time-delayed BAM neural networks under parameter uncertainties

This paper describes a new global robust stability analysis of bidirectional associative memory (BAM) neural networks. Under parameter uncertainty, we find a new upper bound on the norm of the weight matrix of the synaptic connection of time-delayed BAM neural networks. Our new upper bound provides a different kind of sufficient condition for the equilibrium point pertaining to the robust stability of BAM neural networks. Several classes of bounded activation functions are formulated. In addition, appropriate Lyapunov–Krasovskii functional (LKF) candidates are used in the process of deriving the new sufficient conditions for the BAM neural networks that are independent of the time delay parameters. We conduct some comparative studies with numerical examples to demonstrate the advantages of our findings over the stability results in terms of BAM neural network parameters.

Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result.

Global robust stability analysis of uncertain neural networks with time varying delays

This paper deals with the global robust stability analysis of dynamical neural networks with time varying delays. By combining Lyapunov stability theorems and Homeomorphic mapping theorem, we obtain some original sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point with respect to Lipschitz activation functions and under parameter uncertainties of the neural system. We also prove that the obtained robust stability conditions generalize some of the previously published corresponding literature results. The conditions we present can be easily verified as the conditions that are expressed in terms of the network parameters. Some comparative numerical examples are presented to demonstrate the advantages of our conditions over the previously published robust stability results.

Dynamical Nonlinear Neural Networks with Perturbations Modeling and Global Robust Stability Analysis

paper is devoted to studying both the global and local stability of dynamical neural networks. In particular, it has focused on nonlinear neural networks with perturbation. Properties relating to asymptotic and exponential stability and instability have been detailed. This paper also looks at the robustness of neural networks to perturbations and examines if the related properties have been preserved. Circumstances for global and local exponential stability of nonlinear neural network dynamics have been studied. We mentioned that the local exponential stability of any equilibrium point of dynamical neural networks is equivalent to the stability of the linearized system around that equilibrium point. From this, some well-known and new sufficient conditions for local exponential stability of neural networks have been obtained. The Lyapunov's procedure has been used to analyze the stability property of nonlinear dynamical systems and many outcomes have been combined and generalized. A kind of Lyapunov's stability of the stable points of Hopfield neural network (HNN) have been proven, which means that if the initial state of the network is close enough to a stable point, then the network state will remain in a small neighborhood of the stable point. These stability results indicate the convergence of the memory process of HNN. The theoretical results are illustrated through a few problem cases for a nonlinear dynamical system with perturbation behavior. Keywordserturbed nonlinear systems, Hopfield neural network,

Global robust stability analysis for BAM neural networks with time-varying delays

This paper is concerned with the problem of global robust asymptotical stability of the equilibrium point for bidirectional associative memory (BAM) neural networks. The activation functions are assumed to be neither differentiable nor strict monotonic and the delays are time-varying. Furthermore, based on the approach of linear matrix inequality (LMI), a new inequality and Lyapunov–Krasovskii functional are applied to derive the results of robust asymptotical stability. Also, a simulation example is presented to demonstrate the effectiveness and applicability of our results.

New delay-dependent global robust stability conditions for interval neural networks with time-varying delays

This paper deals with the problem of delay-dependent global robust stability analysis for interval neural networks with time-varying delays. By introducing an equivalent transformation of interval systems and the free-weighting matrix technique, a new delay-dependent condition on global robust stability is established. This condition is presented in terms of a linear matrix inequality (LMI), which can be easily checked by using recently developed algorithms in solving LMIs. A numerical example is provided to demonstrate the effectiveness of the proposed method.

A delay-range-dependent approach to global robust stability for discrete-time uncertain recurrent neural networks with interval time-varying delay

The current paper performs a global robust stability analysis for a class of discrete-time recurrent neural networks (DRNNs) with norm-bounded time-varying parameter uncertainties and interval time-varying delay. The activation functions are assumed to be globally Lipschitz continuous. An appropriate type of Lyapunov functional is proposed to establish the sufficient conditions for the DRNNs. The criteria are formulated by means of the feasibility of linear matrix inequalities (LMIs), which can be easily checked in practice. Two numerical examples are given to illustrate the effectiveness and applicability.

Global robust stability analysis of neural networks with multiple time delays

Global robust convergence properties of continuous-time neural networks with discrete delays are studied. By employing suitable Lyapunov functionals, we derive a set of delay-independent sufficient conditions for the existence, uniqueness, and global robust asymptotic stability of the equilibrium point. The conditions can be easily verified as they can be expressed 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. One of our main results is shown to improve and generalize a previously published result. Other results proved to establish a new set of robust stability criteria for delayed neural networks.

Improved Global Robust Asymptotic Stability Criteria for Delayed Cellular Neural Networks

This paper considers the problem of global robust stability analysis of delayed cellular neural networks (DCNNs) with norm-bounded parameter uncertainties. In terms of a linear matrix inequality, a new sufficient condition ensuring a nominal DCNN to have a unique equilibrium point which is globally asymptotically stable is proposed. This condition is shown to be a generalization and improvement over some previous criteria. Based on the stability result, a robust stability condition is developed, which contains an existing robust stability result as a special case. An example is provided to demonstrate the reduced conservativeness of the proposed results.

Global robust stability analysis of neural networks with discrete time delays

Abstract Global robust convergence properties of continuous-time neural networks with discrete delays are studied. By using a Lyapunov functional, we derive a delay independent stability condition for the existence uniqueness and global robust asymptotic stability of the equilibrium point. The condition is in terms of the network parameters only and can be easily verified. It is also shown that the obtained result improves and generalizes a previously published result.