Model reduction by Chebyshev polynomial techniques

Abstract

The problem of reduced-order modeling of high-order, linear, time-invariant, single-input, single-output systems is considered. A method is proposed, based on manipulating two Chebyshev polynomial series, one representing the frequency response characteristics of the high-order system and the other representing the approximating low-order model. The method can be viewed as generalizing the classical Padé approximation problem, with the Chebyshev polynomial series expansion being over a desired frequency interval instead of a power series about a single frequency point. Two different approaches to the problem are considered. Firstly, approximation is carried out in the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">s</tex> -plane by a Chebyshev polynomial series. Then, modified Chebyshev polynomials are introduced and a mapping to a new plane is defined. It turns out that in the new plane the advantages of the generalized Chebyshev-Padé approximations are retained while what is actually being solved is the classical Padé problem.