Quasi-finite-rank approximation of compression operators on L∞[0, h) with application to stability analysis of time-delay systems
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- Title
- Quasi-finite-rank approximation of compression operators on L∞[0, h) with application to stability analysis of time-delay systems
- Authors
- KIM, JUNG HOON; Hagiwara, Tomomichi
- Date Issued
- 2014-01-16
- Publisher
- Institution of Engineering and Technology
- Abstract
- This study discusses a new method for approximating compression operators, which play important roles in the operator-theoretic approach to sampled-data systems and time-delay systems. Stimulated by the success in the application of quasi-finite-rank approximation of compression operators defined on the Hilbert space L-2[0, h), the authors study a parallel problem for compression operators defined on the Banach space L[0, h). In spite of similarity between these problems, they are led to applying a completely different approach because of essential differences in the underlying spaces. More precisely, they apply the idea of the conventional fast-sample/fast-hold (FSFH) approximation technique, and show that the approximation problem can be transformed into such a linear programming problem that asymptotically leads to optimal approximation as the FSFH approximation parameter M tends to infinity. Finally, they demonstrate the effectiveness of the L[0, h)-based approximation technique through numerical examples, with particular application to stability analysis of time-delay systems.
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/98856
- DOI
- 10.1049/iet-cta.2013.0458
- ISSN
- 1751-8644
- Article Type
- Article
- Citation
- IET Control Theory and Applications, vol. 8, no. 2, page. 77 - 85, 2014-01-16
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