Factorization‐based frequency‐weighted optimal Hankel‐norm model reduction

Abstract

In this paper, we present frequency‐weighted optimal Hankel‐norm model reduction algorithms for linear time‐invariant continuous‐time systems by representing an original higher‐order system into new fictitious systems. The new system representations are derived through factorization of the resulting sub‐matrices that are obtained after transformations. As the proposed approaches are factorization dependent, additional results with both approaches are included using another factorization of the fictitious input–output and weight matrices. The proposed algorithms generate stable reduced models with double‐sided weights and provide a substantial improvement in the weighted error. A numerical example is given to compare the efficacy of the proposed algorithms with the well‐known frequency‐weighted techniques.

Comparative analysis of model reduction strategies for circuit based periodic control problems

“…Model reduction of () has been the topic of intensive research in recent years. Attempts have been made to reduce the dimensions of large‐scale systems using balanced truncation [8–12], Krylov‐based projection methods [1, 5, 13–16], the interpolatory method, optimal Hankel norm method, and polynomial method, as seen in [17]. Model reduction algorithms linking both balanced truncation and Krylov‐based methods have also been proposed in [2, 18–21].…”

Coprime factorization of polytopic LPV systems based on a homogeneous polynomial approach

“…Since the publication of Vidyasagar [1], coprime factorization descriptions have been playing an important role for the modern robust control theory regarding both linear and nonlinear systems [2,3]. Much of this interest referred to study of some fundamental problems, such as model reduction [4][5][6], fault detection [7,8], and synthesis of robust stabilizing controllers for linear [9][10][11] and nonlinear systems [12][13][14]. A significant theory that made such results possible is the existence of a special coprime factorization description called normalized coprime factorization, whose right and left coprime factors are obtained, at first, solving algebraic Riccati equations.…”

Model reduction based on limited‐time interval impulse response Gramians

“…Recently, Haider et al [14] proposed the limited‐time Gramians for large‐scale descriptor systems. Some recent developments on frequency band related model reduction are appeared in [16–23].…”