The inverse problem of analytic interpolation with degree constraint

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2006, Pages 559-564

  Karlsson, Johan ^a   Georgiou, Tryphon ^b   Lindquist, Anders ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b University of Minnesota   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION ALGORITHMS; CONSTRAINT THEORY; FUNCTION EVALUATION; INTERPOLATION;

ANALYTIC INTERPOLATION;

INVERSE PROBLEMS;

EID: 39649118367     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2006.376827     Document Type: Conference Paper

References (17)

1. J. Agler, J. E. McCarthy Pick Interpolation and Hubert Function Spaces, American Mathematical Society, 2002.
2. C. I. Byrnes, P. Enqvist, and A. Lindquist, Cepstral coefficients, covariance lags and pole-zero models for finite data strings, IEEE Trans.SP-49 (2001), 677-693.
3. C. I. Byrnes, S. V. Gusev, and A. Lindquist, A convex optimization approach to the rational covariance extension problem, SIAM J. Contr. and Optimiz. 37 (1998) 211-229.
4. C. I. Byrnes, S. V. Gusev, and A. Lindquist, From finite covariance windows to modeling filters: A convex optimization approach, SIAM Review 43 (2001), 645-675.
5. C. I. Byrnes, A. Lindquist, S. V. Gusev, and A. S. Matveev, A complete parameterization of all positive rational extensions of a covariance sequence, IEEE Trans. Automat. Control, 40 (1995), 1841-1857.
6. C. I. Byrnes, T. T. Georgiou, and A. Lindquist, A generalized entropy criterion for Nevanlinna-Pick interpolation with degree constraint, IEEE Trans. Automat. Control 46 (2001), 822-839.
7. ∞ with a complexity constraint," Trans. of the American Math. Society, 358 (2006) no. 3, 965-988). TRANSACTIONS- AMERICAN MATHEMATICAL SOCIETY
8. J.B. Garnett, Bounded analytic Functions, Academic Press, 1981.
9. T.T. Georgiou, Partial Realization of Covariance Sequences, Ph.D. thesis, CMST, University of Florida, Gainesville 1983.
10. T. T. Georgiou, Realization of power spectra from partial covariance sequences, IEEE Trans. Acoustics, Speech and Signal Processing 35 (1987), 438-449.
11. T.T. Georgiou and A. Lindquist, 'Kullback-Leibler approximation of spectral density functions," IEEE Trans. on Information Theory, 49(11), November 2003.
12. T.T. Georgiou and A. Lindquist, Remarks on control design with degree constraint, IEEE Transactions on Automatic Control, to be published.
13. R.E. Kalman, 'When is a linear control system optimal?" Journal of Basic Engineering, pp. 51-60, March 1964.
14. J. Karlsson and A. Lindquist, On complexity constrained interpolation with interpolation points close to the boundary, Proc. MTNS 2006.
15. ∞ Control, Lecture Notes in Control and Information Sciences, 146. Springer-Verlag, Berlin, 1990.
16. M. S. Takyar, A. N. Amini, and T. T. Georgiou, 'Sensitivity shaping with degree constaint via convex optimization" ACC, Jun. 2006.
17. K. C. Sou, A. Megretski, and L. Daniel, 'A quasi-convex optimization approach to parameterized model order reduction," IEEE Proc. on Design Automation Conference, 933-938, Jun. 2005.