Reduction of discrete interval system using clustering of poles with Padé approximation: a computer-aided approach

Abstract

This paper presents a method for the order reduction of discrete interval systems using pole-clustering method along with Padé approximation technique. For a given discrete high-order interval system (HOIS), the denominator of the reduced-order interval model (ROIM) is obtained by pole-clustering while the numerator is obtained by minimizing errors between first r time moments of the HOIS to those of its ROIM where r is the order of ROIM. Inverse distance measure (IDM) criterion is used for clustering of poles of HOIS whereas the time moments of HOIS (or ROIM) are obtained without inverting the denominator of transfer function and presented in generalized form. The error function which is weighted squared sum of errors between first r time moments of HOIS and those of its ROIM is carried out by the algorithm due to Luus-Jaakola. The distinctive feature of this method is that the numerator coefficients are treated free in the process of minimization. A numerical example is given to illustrate the procedure.

Keywords: Discrete interval system; Inverse distance measure; Kharitonov polynomials; Model reduction; Padé approximation; Pole-clustering method