基于二阶近似积分不等式的时滞系统稳定性分析
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TP273

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19Z1240010018


Second-Order Approximation Integral Inequality for Stability of Systems with Time Delays
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The National Natural Science Foundation of China (General Program, Key Program, Major Research Plan)

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    摘要:

    本文提出了一种新的积分不等式,称为二阶近似积分不等式(Second-order Approach Integral Inequality,SAII)。著名的积分不等式如Jensen不等式和基于Wirtinger的不等式均是本文所提的二阶近似积分不等式的特例,并且进一步证明了Jensen不等式和Wirtinger不等式分别是所提不等式的零阶和一阶近似。在所提二阶近似积分不等式基础上,提出了一种适用于时滞系统的稳定性判据。最后,算例表明了该方法的有效性和优越性。

    Abstract:

    This paper proposed a new integral inequality, called second-order approximation integral inequality (SAII), that could significantly reduce the conservativeness in stability analysis of systems with time delays. The former well-known integral inequalities such as Jensen’s inequality and Wirtinger based inequality, are all included in the proposed integral inequality as special cases. Furthermore, it’s shown that Jensen’s and Wirtinger based inequalities are just zero-order and first-order approximation, respectively. Stability criterion with less conservatism is then developed using SAII for time delay systems. Numerical examples are given to demonstrate the effectiveness and benefit of the proposed method.

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王楠,龚德仁,许光坦,等. 基于二阶近似积分不等式的时滞系统稳定性分析[J]. 科学技术与工程, 2020, 20(22): 9097-9101.
WANG Nan, XU Guang-tan, DUAN Deng-ping. Second-Order Approximation Integral Inequality for Stability of Systems with Time Delays[J]. Science Technology and Engineering,2020,20(22):9097-9101.

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历史
  • 收稿日期:2019-11-06
  • 最后修改日期:2020-04-26
  • 录用日期:2020-01-11
  • 在线发布日期: 2020-08-25
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