Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach
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Passivity Analysis of Fractional-Order Neural Networks with Time-Varying Delay Based on LMI Approach Nguyen Huu Sau1 · Mai Viet Thuan2,3
· Nguyen Thi Thanh Huyen4
Received: 16 December 2019 / Revised: 1 May 2020 / Accepted: 5 May 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, we study the problem of passivity analysis of fractional-order neural networks (FONNs) with a time-varying delay. By using the Razumikhin fractionalorder theorem, we first derive an improved sufficient criterion for asymptotic stability of FONNs with a bounded time-varying delay. Then, based on the proposed stability criterion and some auxiliary properties of fractional calculus, a delay-dependent condition is established to ensure the passivity of the considered system. These conditions are order-dependent and in the form of linear matrix inequalities, which therefore can be efficiently solved in polynomial time by using the existing convex algorithms. Some numerical examples are provided to show the effectiveness of the obtained results. Keywords Caputo fractional-order · Neural networks · Asymptotic stability · Passivity analysis · Time-varying delays · Linear matrix inequality
1 Introduction In recent years, FONNs have attracted considerable research attention. Compared with integer-order neural networks (IONNs), FONNs can represent the real dynamic characteristics of actual network systems more accurately. As a consequence, many important and interesting results on FONNs have been reported and various issues
B
Mai Viet Thuan [email protected] Nguyen Huu Sau [email protected]
1
Institute of Research and Development, Duy Tan University, Danang 550000, Vietnam
2
Department for Management of Science and Technology Development, Ton Duc Thang University, Ho Chi Minh City, Vietnam
3
Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
4
Department of Mathematics and Informatics, Thainguyen University of Sciences, Thainguyen, Vietnam
Circuits, Systems, and Signal Processing
have been studied by many authors, such as asymptotic stability [18,19,30,37,47,51], finite-time stability [7,36,41,45,49], guaranteed cost control [39,42], synchronization analysis [1,5,26–29,32,46,52,53,56,57], H∞ control problem [43] and so on. On the other hand, passivity theory plays an important role in network control theory [31]. Passivity performance analysis has also been extensively applied in various areas such as signal processing, fuzzy control, power system, robot system and so on. In the recent years, many important results on passivity analysis for continuous-time or discrete-time integer-order dynamical systems have been reported in the literature [3–5,8,10,14,20,22–24,40,48,50,54,55,58]. For example, by using a second-order Bessel–Legendre inequality, the authors in [58] derived some improved passivity criterion for neural networks with a bounded time-varying delay. The conditions were expressed in terms of linear matrix inequality (LMI).
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