Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems

Hamid Reza Shaker

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

1 Citation (Scopus)
326 Downloads (Pure)

Abstract

The notions of controllability and observability play an important role in different problems within feedback control analysis and design. To verify the controllability and observability of a system, several techniques have been introduced. However, often it is not only important to verify if the system is controllable or observable, but also it is required to know the degree of controllability or observability of the system. Gramian matrices were introduced to address this issue by providing a quantitative measure for controllability and observability. In many applications, the information on the controllability and observability properties of a system is needed within a specific frequency interval rather than the whole frequency-domain. The frequency interval gramians provide such information. While this concept were originally introduced for fixed known systems, it needs to be investigated for the case of uncertain systems. In this paper, we derive upper and lower bounds of frequency interval gramians under perturbations of an A-matrix in the state-space form. These bounds are obtained by solving algebraic Riccati equations. The results are further used to obtain upper and lower bounds of the frequency interval Hankel singular values for perturbed systems.
Original languageEnglish
Title of host publication7th IFAC Symposium on Robust Control Design
Number of pages4
PublisherElsevier
Publication date2012
Pages713-716
ISBN (Print)978-3-902823-03-8
DOIs
Publication statusPublished - 2012
Event7th IFAC Symposium on Robust Control Design - Aalborg, Denmark
Duration: 20 Jun 201222 Jun 2012
Conference number: 7

Conference

Conference7th IFAC Symposium on Robust Control Design
Number7
CountryDenmark
CityAalborg
Period20/06/201222/06/2012
SeriesI F A C Workshop Series
ISSN1474-6670

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Observability
Controllability
Linear systems
Riccati equations
Uncertain systems
Feedback control

Cite this

Shaker, H. R. (2012). Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems. In 7th IFAC Symposium on Robust Control Design (pp. 713-716). Elsevier. I F A C Workshop Series https://doi.org/10.3182/20120620-3-DK-2025.00035
Shaker, Hamid Reza. / Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems. 7th IFAC Symposium on Robust Control Design. Elsevier, 2012. pp. 713-716 (I F A C Workshop Series).
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Shaker, HR 2012, Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems. in 7th IFAC Symposium on Robust Control Design. Elsevier, I F A C Workshop Series, pp. 713-716, 7th IFAC Symposium on Robust Control Design, Aalborg, Denmark, 20/06/2012. https://doi.org/10.3182/20120620-3-DK-2025.00035

Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems. / Shaker, Hamid Reza.

7th IFAC Symposium on Robust Control Design. Elsevier, 2012. p. 713-716 (I F A C Workshop Series).

Research output: Contribution to book/anthology/report/conference proceedingArticle in proceedingResearchpeer-review

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Shaker HR. Upper and Lower Bounds of Frequency Interval Gramians for a Class of Perturbed Linear Systems. In 7th IFAC Symposium on Robust Control Design. Elsevier. 2012. p. 713-716. (I F A C Workshop Series). https://doi.org/10.3182/20120620-3-DK-2025.00035