Model order reduction of interval systems using an arithmetic operation

Kranthi Kumar Deveerasetty and S. K. Nagar

International Journal of Systems Science, 2020, vol. 51, issue 5, 886-902

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 $z = \left ({w + 1} \right ) $z=w+1 and bilinear transformation $z = ({1+w})/({1-w}) $z=(1+w)/(1−w), where $w \ne 1 $w≠1. 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.

Date: 2020
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DOI: 10.1080/00207721.2020.1746433

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