A real Schur form method for modeling singularly perturbed systems

Aldhaheri R.W.; Khalil H.K.

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A real Schur form method for modeling singularly perturbed systems

机译：用于建模奇异摄动系统的真正Schur形式方法

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A method is presented for modeling a two-time-scale system in the singularly perturbed form. The method uses an ordered real Schur decomposition, which can be efficiently computed using standard subroutines from EISPACK. Three results are given. First, it is shown that any two-time-scale system can be modeled in the singularly perturbed form by a transformation into an ordered real Schur form, followed by balancing. Second, under some conditions on the ordered real Schur decomposition, a procedure is given to achieve the modeling task with all fast variables chosen from the original state variables. Third, necessary and sufficient conditions are given to achieve modeling by permutation of the original state variables.

机译：提出了一种以奇摄动形式对两尺度系统进行建模的方法。该方法使用有序实数Schur分解，可以使用EISPACK的标准子例程有效地对其进行计算。给出了三个结果。首先，表明可以通过转换为有序实数Schur形式，然后进行平衡，以任何形式对两个时间尺度的系统进行建模。其次，在有序实数Schur分解的某些条件下，给出了使用从原始状态变量中选择的所有快速变量来完成建模任务的过程。第三，给出了必要的和充分的条件以通过对原始状态变量进行置换来实现建模。

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《IEEE Transactions on Automatic Control》 |1989年第8期|P.856-861|共6页
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Aldhaheri R.W.; Khalil H.K.;
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A real Schur form method for modeling singularly perturbed systems

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