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首页> 外文期刊>Automatic Control, IEEE Transactions on >Contraction Analysis of Nonlinear DAE Systems
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Contraction Analysis of Nonlinear DAE Systems

机译：非线性DAE系统的收缩分析

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摘要

This article studies the contraction properties of nonlinear differential-algebraic equation (DAE) systems. Such systems typically appear as a singular perturbation reduction of a multiple-time-scale differential system. In addition, a given DAE may result from the reduction of many “synthetic” differential systems. We show that an important property of a contracting DAE system is that the reduced system always contracts faster than any synthetic counterpart. At the same time, there always exists a synthetic system, whose contraction rate is arbitrarily close to that of the DAE. Synthetic systems are useful for the analysis of attraction basins of nonlinear DAE systems. As any rational DAE system can be represented in quadratic form, the Jacobian of the synthetic system can be made affine in the system variables. This allows for scalable techniques to construct attraction basin approximations, based on uniformly negative matrix measure conditions for the synthetic system Jacobian.
机译：本文研究了非线性差分 - 代数方程（DAE）系统的收缩特性。这种系统通常看起来是多时间级差动系统的奇异扰动。另外，给定的DAE可以由许多“合成”差分系统的减少来引起。我们表明，契约DAE系统的重要属性是减少系统总始终比任何合成对应物更快地收缩。同时，总是存在一个合成系统，其收缩率任意接近DAE的收缩率。合成系统可用于分析非线性DAE系统的吸引池。由于任何Rational DAE系统可以以二次形式表示，因此可以在系统变量中仿射合成系统的雅各比。这允许基于合成系统Jacobian的均匀负矩阵测量条件来构建吸引盆地近似的可扩展技术。

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