Mean square delay dependent-probability-distribution stability analysis of neutral type stochastic neural networks

The combined Lyapunov functionals method for stability analysis of neutral Cohen-Grossberg neural networks with multiple delays

This research article will employ the combined Lyapunov functionals method to deal with stability analysis of a more general type of Cohen-Grossberg neural networks which simultaneously involve constant time and neutral delay parameters. By utilizing some combinations of various Lyapunov functionals, we determine novel criteria ensuring global stability of such a model of neural systems that employ Lipschitz continuous activation functions. These proposed results are totally stated independently of delay terms and they can be completely characterized by the constants parameters involved in the neural system. By making some detailed analytical comparisons between the stability results derived in this research article and the existing corresponding stability criteria obtained in the past literature, we prove that our proposed stability results lead to establishing some sets of stability conditions and these conditions may be evaluated as different alternative results to the previously reported corresponding stability criteria. A numerical example is also presented to show the applicability of the proposed stability results.

Robust Stability Analysis of Delayed Stochastic Neural Networks via Wirtinger-Based Integral Inequality

We discuss stability analysis for uncertain stochastic neural networks (SNNs) with time delay in this letter. By constructing a suitable Lyapunov-Krasovskii functional (LKF) and utilizing Wirtinger inequalities for estimating the integral inequalities, the delay-dependent stochastic stability conditions are derived in terms of linear matrix inequalities (LMIs). We discuss the parameter uncertainties in terms of norm-bounded conditions in the given interval with constant delay. The derived conditions ensure that the global, asymptotic stability of the states for the proposed SNNs. We verify the effectiveness and applicability of the proposed criteria with numerical examples.

An improved Lyapunov functional with application to stability of Cohen-Grossberg neural networks of neutral-type with multiple delays

The essential objective of this research article is to investigate stability issue of neutral-type Cohen-Grossberg neural networks involving multiple time delays in states of neurons and multiple neutral delays in time derivatives of states of neurons in the network. By exploiting a modified and improved version of a previously introduced Lyapunov functional, a new sufficient stability criterion is obtained for global asymptotic stability of Cohen-Grossberg neural networks of neutral-type possessing multiple delays. The proposed new stability condition does not involve the time and neutral delay parameters. The obtained stability criterion is totally dependent on the system elements of Cohen-Grossberg neural network model. Moreover, the validity of this novel global asymptotic stability condition may be tested by only checking simple appropriate algebraic equations established within the parameters of the considered neutral-type neural network. In addition, an instructive numerical example is presented to indicate the advantages of our proposed stability result over the existing literature results obtained for stability of various classes of neutral-type neural networks having multiple delays.

New criteria for global stability of neutral-type Cohen-Grossberg neural networks with multiple delays

The significant contribution of this paper is the addressing the stability issue of neutral-type Cohen-Grossberg neural networks possessing multiple time delays in the states of the neurons and multiple neutral delays in time derivative of states of the neurons. By making the use of a novel and enhanced Lyapunov functional, some new sufficient stability criteria are presented for this model of neutral-type neural systems. The obtained stability conditions are completely dependent of the parameters of the neural system and independent of time delays and neutral delays. A constructive numerical example is presented for the sake of proving the key advantages of the proposed stability results over the previously reported corresponding stability criteria for Cohen-Grossberg neural networks of neutral type. Since, stability analysis of Cohen-Grossberg neural networks involving multiple time delays and multiple neutral delays is a difficult problem to overcome, the investigations of the stability conditions of the neutral-type the stability analysis of this class of neural network models have not been given much attention. Therefore, the stability criteria derived in this work can be evaluated as a valuable contribution to the stability analysis of neutral-type Cohen-Grossberg neural systems involving multiple delays.

Some generalized global stability criteria for delayed Cohen-Grossberg neural networks of neutral-type

This paper carries out a theoretical investigation into the stability problem for the class of neutral-type Cohen-Grossberg neural networks with discrete time delays in states and discrete neutral delays in time derivative of states. By employing a more general type of suitable Lyapunov functional, a set of new generalized sufficient criteria are derived for the global asymptotic stability of delayed neural networks of neutral-type. The proposed stability criteria are independently of the values of the time delays and neutral delays, and they completely rely on some algebraic mathematical relationships involving the values of the elements of the interconnection matrices and the other network parameters. Therefore, it is easy to verify the validity of the obtained results by simply using some algebraic equations representing the stability conditions. A detailed comparison between our proposed results and recently reported corresponding stability results is made, proving that the results given in this paper generalize previously published stability results. A constructive numerical example is also given to demonstrate the applicability of the results of the paper.

Further triple integral approach to mixed-delay-dependent stability of time-delay neutral systems

This paper studies the asymptotic stability for a class of neutral systems with mixed time-varying delays. Through utilizing some Wirtinger-based integral inequalities and extending the convex combination technique, the upper bound on derivative of Lyapunov-Krasovskii (L-K) functional can be estimated more tightly and three mixed-delay-dependent criteria are proposed in terms of linear matrix inequalities (LMIs), in which the nonlinearity and parameter uncertainties are also involved, respectively. Different from those existent works, based on the interconnected relationship between neutral delay and state one, some novel triple integral functional terms are constructed and the conservatism can be effectively reduced. Finally, two numerical examples are given to show the benefits of the proposed criteria.