Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

Stojanovic Sreten; Stojanovic Milan; Stevanovic Milos

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Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

机译：具有时变时滞的离散神经网络的新型时滞相关稳定性准则

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The delay-dependent stability problem is investigated for discrete-time neural networks with time-varying delays. A new augmented Lyapunov-Krasovskii functional (LKF) with single and double summation terms and several augmented vectors is proposed by decomposing the time-delay interval into two nonequidistant subintervals to derive less conservative stability conditions. Then, by using Wirtinger-based inequality, reciprocally, and extended reciprocally convex combination lemmas, tight estimations for sum terms in the forward difference of the LKF are given. Several zero equalities are introduced to further relax the existing results. Less conservative stability criteria are proposed in terms of linear matrix inequalities (LMIs). Finally, numerical examples are proposed to show the effectiveness and less conservativeness of the proposed method.

机译：研究具有时变时滞的离散时间神经网络的时滞相关稳定性问题。通过将时延间隔分解为两个非等距的子间隔，以得出保守性较差的稳定条件，提出了一种新的具有单和双和项和几个增广矢量的增强Lyapunov-Krasovskii泛函（LKF）。然后，通过使用基于Wirtinger的不等式，进行倒数和扩展的倒凸组合引理，给出LKF正向差中和项的严格估计。引入了几个零等式以进一步放松现有结果。根据线性矩阵不等式（LMI），提出了较为保守的稳定性标准。最后，通过算例说明了该方法的有效性和保守性。

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《Mathematical Problems in Engineering》 |2018年第15期|5397870.1-5397870.15|共15页
作者
Stojanovic Sreten; Stojanovic Milan; Stevanovic Milos;
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Univ Nis Fac Technol Dept Engn Sci & Appl Math Bulevar Oslobodjenja 124 Leskovac 16000 Serbia;

Univ Belgrade Sch Elect Engn Dept Syst Control & Signal Proc Bulevar Kralja Aleksandra 73 Belgrade 11000 Serbia|Vlatacom Inst Ltd Bulevar Milutina Milankovica 5 Belgrade 11000 Serbia;

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2. Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays [J] . O. M.Kwon, M. J.Park, Ju H.Park, Abstract and applied analysis . 2012,第3期

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3. Improved Delay-dependent Exponential Stability Criteria For Discrete-time Recurrent Neural Networks With Time-varying Delays [J] . Baoyong Zhang, Shengyuan Xu, Yun Zou Neurocomputing . 2008,第1a3期

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5. Exponential Stability of Intrinsically Stable Dynamical Networks and Switched Networks with Time-Varying Time Delays [D] . Reber, David Patrick. 2019

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6. Design of delay-dependent state estimator for discrete-time recurrent neural networks with interval discrete and infinite-distributed time-varying delays [O] . Chin-Wen Liao, Chien-Yu Lu 2011

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7. Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays [O] . O. M. Kwon, M. J. Park, Ju H. Park, 2012

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Novel Delay-Dependent Stability Criteria for Discrete-Time Neural Networks with Time-Varying Delay

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