Model order reduction of interval systems using an arithmetic operation

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 (Formula presented.) and bilinear transformation (Formula presented.), where (Formula presented.). 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. © 2020, © 2020 Informa UK Limited, trading as Taylor & Francis Group.