Stability Analysis for Neural Networks With Time-Varying Delay via Improved Techniques

This paper is concerned with the stability problem for neural networks with a time-varying delay. First, an improved generalized free-weighting-matrix integral inequality is proposed, which encompasses the conventional one as a special case. Second, an improved Lyapunov-Krasovskii functional is constructed that contains two complement triple-integral functionals. Third, based on the improved techniques, a new stability condition is derived for neural networks with a time-varying delay. Finally, two widely used numerical examples are given to demonstrate that the proposed stability condition is very competitive in both conservatism and complexity.

Delay-Dependent Global Exponential Stability for Delayed Recurrent Neural Networks

This paper deals with the global exponential stability for delayed recurrent neural networks (DRNNs). By constructing an augmented Lyapunov-Krasovskii functional and adopting the reciprocally convex combination approach and Wirtinger-based integral inequality, delay-dependent global exponential stability criteria are derived in terms of linear matrix inequalities. Meanwhile, a general and effective method on global exponential stability analysis for DRNNs is given through a lemma, where the exponential convergence rate can be estimated. With this lemma, some global asymptotic stability criteria of DRNNs acquired in previous studies can be generalized to global exponential stability ones. Finally, a frequently utilized numerical example is carried out to illustrate the effectiveness and merits of the proposed theoretical results.

Stability for neural networks with time-varying delays via some new approaches

This paper considers the problem of delay-dependent stability criteria for neural networks with time-varying delays. First, by constructing a newly augmented Lyapunov-Krasovskii functional, a less conservative stability criterion is established in terms of linear matrix inequalities. Second, by proposing novel activation function conditions which have not been proposed so far, further improved stability criteria are proposed. Finally, three numerical examples used in the literature are given to show the improvements over the existing criteria and the effectiveness of the proposed idea.

Stability analysis of multiplicative update algorithms and application to nonnegative matrix factorization

Multiplicative update algorithms have proved to be a great success in solving optimization problems with nonnegativity constraints, such as the famous nonnegative matrix factorization (NMF) and its many variants. However, despite several years of research on the topic, the understanding of their convergence properties is still to be improved. In this paper, we show that Lyapunov's stability theory provides a very enlightening viewpoint on the problem. We prove the exponential or asymptotic stability of the solutions to general optimization problems with nonnegative constraints, including the particular case of supervised NMF, and finally study the more difficult case of unsupervised NMF. The theoretical results presented in this paper are confirmed by numerical simulations involving both supervised and unsupervised NMF, and the convergence speed of NMF multiplicative updates is investigated.