A frequency-weighted discrete system balanced truncation method and an error bound

Campbell, Kevin W.; Sreeram, Victor; Wang, G.

doi:10.1109/acc.2000.878611

Cited by 11 publications

(42 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section we review some of the existing frequency weighted model reduction techniques for discrete time systems which include Enns [25], Campbell et al 's [37], and Varga and Anderson's [38].…”

Section: Preliminariesmentioning

confidence: 99%

“…It is not guaranteed to ensure that ≥ 0 and ≥ 0; the reduced order models obtained using Enns technique may not remain stable for both sided weightings. [37]. Campbell et al 's [37] (a discrete time version of [28]) guarantees the positive semidefiniteness of symmetric matrices and to ensure stability.…”

Section: Preliminariesmentioning

confidence: 99%

“…Most frequently, frequency weighted model reduction problem is treated in continuous time; however, there are few papers (like [36][37][38]) which deal with this problem explicitly in discrete time. Sahlan et al 's [36] technique (discrete time version of [31]) is a modified version of Lin and Chiu [27] technique.…”

Section: Introductionmentioning

confidence: 99%

“…Sahlan et al 's [36] technique (discrete time version of [31]) is a modified version of Lin and Chiu [27] technique. Campbell et al 's [37] technique is discrete time counterpart of Wang et al 's [28] technique, which not only provides stability for two sided case but also gives easily computable error bounds. Campbell et al 's [37] technique involves taking absolute values of eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

“…Campbell et al 's [37] technique is discrete time counterpart of Wang et al 's [28] technique, which not only provides stability for two sided case but also gives easily computable error bounds. Campbell et al 's [37] technique involves taking absolute values of eigenvalues. This may introduce a large change to the system and hence a larger error if it contains some negative eigenvalues.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems

Imran¹,

Ghafoor

Sreeram³

2014

Mathematical Problems in Engineering

View full text Add to dashboard Cite

Model reduction is a process of approximating higher order original models by comparatively lower order models with reasonable accuracy in order to provide ease in design, modeling and simulation for large complex systems. Generally, model reduction techniques approximate the higher order systems for whole frequency range. However, certain applications (like controller reduction) require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case) and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.

show abstract

Section: Preliminariesmentioning

confidence: 99%