Singular value analysis of Hankel operators for general nonlinear systems
Singular value analysis of Hankel operators for general nonlinear systems
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一般非线性系统Hankel算子的奇异值分析
DOI：
10.23919/ecc.2003.7085041
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
J. Scherpen
中科院分区：
文献类型：
--
作者：
K. Fujimoto;J. Scherpen
本文讨论了一般非线性系统的连续和离散Hankel算子的奇异值分析。奇异值分析阐明了给定算子的增益结构。本文证明了定义在Hilbert空间上的光滑Hankel算子的奇异值分析可以用简单的状态方程来刻画。在此基础上推导了一种平衡和模型降阶方法，特别是当该方法应用于连续时间非线性系统时，保持了系统的Hankel范数、能控性和能观性等增益特性。
This paper discusses singular value analysis of Hankel operators for both continuous-time and discrete-time general nonlinear systems. Singular value analysis clarifies the gain structure of a given operator. Here it is proven that singular value analysis of smooth Hankel operators defined on Hilbert spaces can be characterized by simple equations in terms of their states. A balancing and model reduction procedure is derived based on it. In particular, when the proposed model reduction method is applied to continuous-time nonlinear systems, several gain properties such as Hankel norm, controllability and observability functions are preserved.