Semidefinite Hankel-Type Model Reduction Based on Frequency Response Matching

Abstract

This paper is dedicated to model order reduction of linear time-invariant systems. The main contribution of this paper is the derivation of two scalable stability-preserving model reduction algorithms. Both algorithms constitute a development of a recently proposed model reduction method. The algorithms perform a curve fitting procedure using frequency response samples of a model and semidefinite programming methods. Computation of these samples can be done efficiently even for large scale models.Both algorithms are obtained from a reformulation of the model reduction problem. One proposes a semidefinite relaxation, while the other is an iterative semidefinite approach. The relaxation approach is similar to Hankel model reduction, which is a well-known and established method in the control literature. Due to this resemblance, the accuracy of approximation is also similar to the one of Hankel model reduction. An appealing quality of the proposed algorithms is the ability to easily perform extensions, e.g., introduce frequency-weighting, positive-real and bounded-real constraints.

Model Reduction of Discrete-Time Interval Type-2 T–S Fuzzy Systems

“…Besides, in the past few decades, many methods have been introduced for solving the problem of model reduction such as Hankel norm based methods [39], [40], H ∞ norm based methods [41], [42], H 2 norm based methods [43], and H 2 -H ∞ based methods [44]. In addition, some other methods such as balanced truncation approach [45], [46] and frequency response matching [47] have also been proposed. For model reduction of type-1 FMB systems, there have been some research results reported in recent years.…”

Model reduction of discrete Markovian jump systems with time‐weighted H2 performance

“…On the other hand, mathematical modeling of physical systems often results in high‐order models and it is desirable to replace these high‐order models with reduced ones with respect to some given criteria. This has motivated the study of the model reduction problem with various approaches . For the model reduction problems of MJLS, the efforts are mainly concentrated on three kinds of reduction problems, namely, classical balanced truncation model reduction, H ∞ model reduction, and H 2 model reduction.…”

Reduced-order fuzzy modeling for nonlinear switched systems

“…In the past two decades, the issue of model reduction has been paid considerable attention. There are an army of efficient approaches to settle the difficulty of model reduction, such as the optimal H 2 approach [19], the H ∞ approach [14], [18], the L 2 -L ∞ approach [6] and the optimal Hankel-norm approach [13]. The model reduction problem with a Hankelnorm sense has been investigated by numerous researchers.…”