Abstract
This study is concerned with the problem of new delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays via introducing a novel integral inequality approach. Specifically, first, by taking fully the relationship between the terms in the Leibniz-Newton formula into account, several improved delay-dependent exponential stability criteria are obtained in terms of linear matrix inequalities (LMIs). Second, together with some effective mathematical techniques and a convex optimization approach, less conservative conditions are derived by constructing an appropriate Lyapunov-Krasovskii functional (LKF). Third, the proposed methods include the least numbers of decision variables while keeping the validity of the obtained results. Finally, three numerical examples with simulations are presented to illustrate the validity and advantages of the theoretical results.
Highlights
Over the course of the past decade, neural networks have become an important area of research and attracted increasing attention due to their extensive applications in many practical systems, such as power systems [1], pattern recognition [2], signal detection [3], landmark recognition [4], and other scientific areas [5,6,7]
It is inevitable to introduce time delay into the signals transmitted among neurons because the processes of transcription and translation are not instantaneous. It is a well-known fact that time delay as a source of instability and poor performance usually appears in many dynamical systems, for instance, Cohen-Grossberg neural networks, cellular neural networks, BAM neural network, chaotic neural networks, H∞ filtering, and nonlinear systems [8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53]
By using a new integral inequality approach to express the relationship between the terms in the LeibnizNewton formula within the framework of linear matrix inequality (LMI) for the first time, several less conservative delay-dependent exponential stability criteria are obtained
Summary
Over the course of the past decade, neural networks have become an important area of research and attracted increasing attention due to their extensive applications in many practical systems, such as power systems [1], pattern recognition [2], signal detection [3], landmark recognition [4], and other scientific areas [5,6,7]. Motivated by the above discussion, combining effective mathematical techniques and a convex optimization approach, we choose a more general type of LKF to study the delay-dependent exponential stability criteria for neural networks (NNs) with mixed time-varying delays in the paper. Some improved delay-dependent stability conditions derived benefit mainly from using firstly a new integral inequality approach, which is proved to be less conservative than the celebrated Jensen’s inequality and showed having a great potential efficient in practice. Both theoretical and numerical comparisons have been provided to show the effectiveness and efficiency of the proposed method.
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