2-D model reduction by quasi-balanced truncation and singular perturbation

Zhou, Kemin; Aravena, J.L.; Gu, Guoxiang; Xiong, Daxi

doi:10.1109/82.326586

Cited by 41 publications

(13 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is well known that the reduced models derived from the Badreddin and Mansour method [2] or the balanced truncation method [15] are stable if the 1-D original system is stable. However, in contrast to the 1-D case, in these 2-D extensions [10,13,21] the stability of the reduced-order models are not generally guaranteed even for a stable full-order system.…”

Section: Introductionmentioning

confidence: 85%

See 1 more Smart Citation

Optimal 2-D Separable-Denominator Approximants for 2-D Transfer Functions

Guo¹,

Guo

1997

Journal of the Chinese Institute of Engineers

View full text Add to dashboard Cite

This paper is concerned with the optimal approximation of a general 2-D transfer function by a separable-denominator one with stability preservation. To preserve the stability, the two one-variable denominator polynomials of the reduced model are both represented in their bilinear Routh continued-fraction expansions. The bilinear Routh .Yparameters of the two one-variable denominator polynomials and the coefficients of the two-variable numerator polynomial are then determined such that a frequency-domain L 2 -norm is minimized. The main advantage of searching bilinear Routh .Yparameters instead of denominator coefficients is that the stability constraints on the new decision parameters are simple bounds. To facilitate using a gradient-based algorithm, an effective numerical algorithm is also provided for computing the performance index and its gradients with respect to the decision variables. 213

show abstract

Section: Introductionmentioning

confidence: 85%

“…al. [21] utilized the singular perturbation reduction technique [3] to a quasi-balanced realization and obtained a singular perturbation approximant. It is well known that the reduced models derived from the Badreddin and Mansour method [2] or the balanced truncation method [15] are stable if the 1-D original system is stable.…”

Section: Introductionmentioning

confidence: 99%

Optimal 2-D Separable-Denominator Approximants for 2-D Transfer Functions

Guo¹,

Guo

1997

Journal of the Chinese Institute of Engineers

View full text Add to dashboard Cite

show abstract

“…In such a case, the points defined by (9) need to be modified to (13) where denotes the radius of a circle in the plane where has no eigenvalues. With , (10) (14) Note that (12) is a special case of (14) with , as may be expected.…”

Section: B the Unstable Casementioning

confidence: 99%

“…Obviously, Algorithm 4 can be used to evaluate only if matrices and have no eigenvalues on the unit circle. If matrix or has eigenvalues on the unit circle, then modifications similar to (13), (14) should be made.…”

Section: B Dual Algorithmmentioning

confidence: 99%

“…These include methods for stability analysis [2]- [6], analysis of finite-wordlength effects [7], [8], design [9], [10], model reduction [11]- [13], and relevant computation issues [14], [15]. Since many of the available analysis and design methods are applicable only to the 2-D transfer-function matrix, it is often necessary to derive the transfer-function matrix from a state-space description of the system.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

New algorithms for the derivation of the transfer-function matrices of 2-D state-space discrete systems

Luo¹,

Antoniou

1997

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

Two‐dimensional FIR filters model order reduction and frequency transformation: Maximum error invariance

Bouhamla¹,

Adamou‐Mitiche²,

Mitiche³

2019

Int J Numerical Modelling

View full text Add to dashboard Cite

This paper presents a numerical study of the maximum error in model order reduction (MOR) for finite impulse response (FIR) 2‐D digital filter under frequency transformation, which is based on the Roesser state‐space formulation. This study discuss the maximum error obtained from the 2‐D balanced truncation method after and before using the frequency transformation. Several numerical examples are realized to show the invariant of the maximum error in all frequency transformation cases (single variable, two‐variable, and hybrid variable transformations).

show abstract

2-D model reduction by quasi-balanced truncation and singular perturbation

Cited by 41 publications

References 20 publications

Optimal 2-D Separable-Denominator Approximants for 2-D Transfer Functions

Optimal 2-D Separable-Denominator Approximants for 2-D Transfer Functions

New algorithms for the derivation of the transfer-function matrices of 2-D state-space discrete systems

Two‐dimensional FIR filters model order reduction and frequency transformation: Maximum error invariance

Contact Info

Product

Resources

About