ABSTRACT The paper presents an extension of the differentiation method for model order reduction of large-scale interval systems. This is an alternative approach to the existing differentiation method of interval systems. The proposed method has been applied for both continuous and discrete-time interval systems. The reduction of discrete-time interval systems is achieved by using simple linear transformation and bilinear transformation , where . The proposed method always generates stable reduced-order models, and also it retains the zeroth-order interval time moment. Four numerical examples exemplify the accuracy of the method and computational simplicity. Furthermore, the difficulties associated with the extension of Routh-based approximations to interval systems for obtaining stable reduced-order models are discussed. The stability of interval systems is verified by using Kharitonov's theorem.

中文翻译：

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使用算术运算对区间系统进行模型降阶

摘要 本文提出了一种用于大规模区间系统模型降阶的微分方法的扩展。这是现有区间系统微分方法的替代方法。所提出的方法已应用于连续和离散时间间隔系统。离散时间间隔系统的约简是通过使用简单的线性变换和双线性变换来实现的，其中 。所提出的方法始终生成稳定的降阶模型，并且还保留了零阶间隔时间矩。四个数值例子说明了该方法的准确性和计算的简单性。此外，讨论了与将基于劳斯的近似扩展到区间系统以获得稳定的降阶模型相关的困难。