Abstract
The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated. Based on a suitable Lyapunov–Krasovskii functional (LKF), an improved Wirtinger single integral inequality, a novel triple integral inequality, and convex combination technique, the new asymptotic stability and extended dissipativity criteria are achieved for the generalized neural networks with interval discrete and distributed time-varying delays. By the above methods, the less conservative asymptotic stability criteria are obtained for a special case of the generalized neural networks. By using the Matlab LMI toolbox, the derived new asymptotic stability and extended dissipativity criteria are expressed in terms of linear matrix inequalities (LMIs) that cover H_{infty }, L_{2}–L_{infty }, passivity, and dissipativity performance by setting parameters in the general performance index. Finally, we show numerical examples which are less conservative than other examples in the literature. Moreover, we present numerical examples for asymptotic stability and extended dissipativity performance of the generalized neural networks, including a special case of the generalized neural networks.
Highlights
In the numerous science and engineering fields, neural networks (NNs) have been studied extensively in recent years due to the wide range of their applications such as in signal processing, fault diagnosis, pattern recognition, associative memory, reproducing moving pictures, optimization problems, and industrial automation [1,2,3,4,5]
It is well known that the time delay always occurs in real world situations, and it causes oscillation, instability, and poor performance of the system
The time delay in neural networks is caused by the finite speed of information processing and the communication time of neurons
Summary
In the numerous science and engineering fields, neural networks (NNs) have been studied extensively in recent years due to the wide range of their applications such as in signal processing, fault diagnosis, pattern recognition, associative memory, reproducing moving pictures, optimization problems, and industrial automation [1,2,3,4,5]. Many studies have separated the stability or performance of LFNNs and SNNs. For example, Zeng et al [11] investigated the stability and dissipativity problem of static neural networks with interval time-varying delay. In [20], the problem of finite-time nonfragile passivity control for neural networks with time-varying delay is investigated based on a new Lyapunov–Krasovskii function with tripple and quadruple integral terms and utilizing Wirtinger-type inequality technique. The extended dissipative analysis was studied for the GNNs with interval time-varying delay signals [37]. It is interesting to study the extended dissipativity performance for GNNs with interval discrete and distributed time-varying delays, which has not been studied, yet. The problem of asymptotic stability and extended dissipativity analysis for the generalized neural networks with interval discrete and distributed time-varying delays is investigated in this paper.
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