Model Reduction of Neutral Linear and Nonlinear Time-Invariant Time-Delay Systems With Discrete and Distributed Delays
Model Reduction of Neutral Linear and Nonlinear Time-Invariant Time-Delay Systems With Discrete and Distributed Delays
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DOI：
10.1109/tac.2015.2461093
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发表时间：
2016-06
影响因子：
6.8
通讯作者：
G. Scarciotti;A. Astolfi
中科院分区：
文献类型：
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作者：
G. Scarciotti;A. Astolfi
研究了线性和非线性微分时滞系统的矩匹配模型降维问题。所考虑的模型类别包括具有离散延迟和分布式延迟的中性微分时滞系统。通过线性时滞系统的类西尔维斯特方程和非线性时滞系统的中心流形理论重新审视了力矩的描述。此外，线性和非线性时滞系统都具有无穷远矩的特征。给出了实现矩匹配的参数化模型族。可以利用这些参数来导出具有附加属性的无延迟降阶模型或时滞降阶模型，例如在任意大量点处进行插值。最后讨论并解决了不稳定系统降阶模型的获取问题。
The problem of model reduction by moment matching for linear and nonlinear differential time-delay systems is studied. The class of models considered includes neutral differential time-delay systems with discrete-delays and distributed-delays. The description of moment is revisited by means of a Sylvester-like equation for linear time-delay systems and by means of the center manifold theory for nonlinear time-delay systems. In addition the moments at infinity are characterized for both linear and nonlinear time-delay systems. Parameterized families of models achieving moment matching are given. The parameters can be exploited to derive delay-free reduced order models or time-delay reduced order models with additional properties, e.g., interpolation at an arbitrary large number of points. Finally, the problem of obtaining a reduced order model of an unstable system is discussed and solved.