Stability of Linear Neutral Time-Delay Systems: Exact Conditions via Matrix Pencil Solutions

Peilin Fu; Silviu-Iulian Niculescu; Tie Chen

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Stability of Linear Neutral Time-Delay Systems: Exact Conditions via Matrix Pencil Solutions

机译：线性中性时滞系统的稳定性：通过矩阵笔解决方案的精确条件

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In this note, we study the stability properties of linear neutral delay systems. We consider systems described by both neutral differential-difference and state-space equations, and we seek to determine the delay margin of such systems, that is, the largest range of delay values for which a neutral delay system may preserve its stability. In both cases, we show that the delay margin can be found by computing the eigenvalues and generalized eigenvalues of certain constant matrices, which can be executed efficiently and with high precision. The results extend previously known work on retarded systems, and demonstrate that similar stability tests exist for neutral systems; in particular, the tests require essentially the same amount of computation required for retarded systems.

机译：在本文中，我们研究了线性中立时滞系统的稳定性。我们考虑由中立差分方程和状态空间方程描述的系统，并试图确定此类系统的延迟裕度，即中性延迟系统可以为其保持稳定性的最大延迟值范围。在这两种情况下，我们都表明，可以通过计算某些恒定矩阵的特征值和广义特征值来找到延迟裕量，这些特征值可以高效，高精度地执行。结果扩展了先前在减速系统上的已知工作，并证明了对于中性系统也存在类似的稳定性测试。特别是，这些测试需要的系统所需的计算量基本相同。

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来源
《IEEE Transactions on Automatic Control》 |2006年第6期|p.1063-1069|共7页
作者
Peilin Fu; Silviu-Iulian Niculescu; Tie Chen;
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正文语种 eng
中图分类自动化系统;
关键词
Delay margin; Matrix pencil; Neutral delay systems; Stability; Time delay;

机译：延迟余量;矩阵笔;中性延迟系统;稳定性;时间延迟;

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1. Delay-dependent stability criterion for neutral time-delay systems via linear matrix inequality approach [J] . Fan KK., Chen JD., Lien CH., Journal of Mathematical Analysis and Applications . 2002,第2期

机译：中立型时滞系统基于线性矩阵不等式的时滞相关稳定性判据
2. Necessary conditions of exponential stability for a class of linear neutral-type time-delay systems [J] . Zhang Xian, Zhao Ning, Shi Peng International Journal of Control . 2019,第4a6期

机译：一类线性中性型时滞系统的指数稳定性条件
3. Asymptotic Stability Conditions and Estimates of Solutions for Nonlinear Multiconnected Time-Delay Systems [J] . Aleksandrov Alexander, Aleksandrova Elena, Zhabko Alexey Circuits, systems, and signal processing . 2016,第10期

机译：非线性多连接时滞系统的渐近稳定性条件和解的估计
4. Stability of Linear Neutral Time-Delay Systems: Exact Conditions via Matrix Pencil Solutions [C] . Peilin Fu, Silviu-Iulian Niculescu, Jie Chen American Control Conference . 2005

机译：线性中性时间延迟系统的稳定性：通过矩阵铅笔解决方案的确切条件
5. Control-Parameter-Space Classification for Delay-Independent-Stability of Linear Time-Invariant Time-Delay Systems; Theory and Experiments. [D] . Nia, Payam Mahmoodi. 2014

机译：线性时不变时滞系统时滞稳定性的控制参数空间分类理论与实验。
6. Stability criteria on delay-dependent robust stability for uncertain neutral stochastic nonlinear systems with time-delay [O] . Tengyu Ma, Longsuo Li -1

机译：具有时滞的不确定中立随机非线性系统的时滞相关鲁棒稳定性的稳定性判据
7. Delay-dependent stability criterion for neutral time-delay systems via linear matrix inequality approach [O] . Fan Kuo-Kuang, Chen Jenq-Der, Lien Chang-Hua, 2002

机译：中立型时滞系统基于线性矩阵不等式的时滞相关稳定性判据

Stability of Linear Neutral Time-Delay Systems: Exact Conditions via Matrix Pencil Solutions

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