Many of the commonly used methods in model‐order reduction do not guarantee stability of the reduced‐order model. This article extends the eigenvalue reassignment method of stabilization of linear time‐invariant ROMs, to the more general case of linear time‐varying systems. Through a postprocessing step, the ROM is controlled to ensure the stability while enhancing/maintaining its accuracy using a constrained nonlinear lease‐square minimization problem. The controller and the input signals are defined at the algebraic level, using left and right singular vectors of the reduced system matrices. The choice provides a control on the upper bound of the growth of the energy of the reduced system. The optimization problem is applied to several time‐invariant, time‐periodic, and time‐varying problems, and the reproductive and predictive capabilities of the proposed method, with respect to novel inputs and the system parameters, are evaluated.

中文翻译：

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线性时变降阶模型的稳定：一种反馈控制器方法

模型顺序约简中的许多常用方法不能保证简化阶模型的稳定性。本文将线性时不变ROM的稳定化特征值重分配方法扩展到线性时变系统的更一般情况。通过后处理步骤，通过约束非线性最小二乘最小化问题，可以控制ROM以确保稳定性，同时提高/保持其准确性。使用简化系统矩阵的左和右奇异矢量，在代数级别定义控制器和输入信号。该选择提供了对简化系统能量增长的上限的控制。优化问题适用于多个时不变，时周期性和时变问题，