Hankel singular values and vectors of a class of infinite-dimensional systems: Exact Hamiltonian formulas for control and approximation problems

Mathematics of Control, Signals, and Systems

Volumn 12, Issue 4, 1999, Pages 361-375

  Ohta, Yoshito ^a  

^a OSAKA UNIVERSITY   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL MODELS; SENSITIVITY ANALYSIS; TRANSFER FUNCTIONS; VECTORS;

HANKEL OPERATOR; HANKEL SINGULAR VALUE; HANKEL SINGULAR VECTOR; INFINITE-DIMENSIONAL SYSTEMS;

MATHEMATICAL OPERATORS;

EID: 0033313712     PISSN: 09324194     EISSN: None     Source Type: Journal    
DOI: 10.1007/PL00009857     Document Type: Article

References (16)

1. B. Bamieh, J. B. Pearson, B. A. Francis, and A. Tannenbaum, A lifting technique for linear periodic systems with applications to sampled-data control, Systems & Control Letters, 17 (1991), 79-88.
2. H. Dym, T. T. Georgiou, and M. C. Smith, Explicit formulas for optimally robust controllers for delay systems, IEEE Transactions on Automatic Control, 40 (1995), 656-669.
3. ∝ sensitivity minimization for delay systems, Systems & Control Letters, 9 (1987), 17-24.
4. ∝ Control Theory, Springer-Verlag, New York, 1987.
5. K. Glover, R. F. Curtain, and J. R. Partington, Realisation and approximation of linear infinite dimensional systems with error bounds, SIAM J. on Control and Optimization, 26 (1988), 863-898.
6. K. Glover, J. Lam, and J. R. Partington, Rational approximation of a class of infinite-dimensional systems, I: singular values of Hankel operators, Mathematics of Control, Signals, and Systems, 3 (1990), 325-344.
7. ∝ and rational weights, Linear Algebra and its Applications, 109 (1988), 71-90.
8. Y. Ohta, Hankel singular values and vectors of a class of infinite dimensional systems for control and approximation problems, Proceedings of the 36th IEEE Conference on Decision and Control, San Diego, 1997, pp. 2765-2770.
9. Y. Ohta and A. Kojima, Formulas for Hankel singular values and vectors for a class of input delay systems, Automatica, 35 (1999), 201-215.
10. H. Özbay, A simpler formula for the singular values of a certain Hankel operator, Systems & Control Letters, 15 (1990), 381-390.
11. M. C. Smith, Singular values and vectors of a class of Hankel operators. Systems & Control Letters, 12 (1989), 301-308.
12. ∝ optimality criterion, Automatica, 28 (1992), 45-54.
13. Y. Yamamoto, A function space approach to sampled data control systems and tracking problems, IEEE Transactions on Automatic Control, 39 (1994), 703-714.
14. ∝ problem, Systems & Control Letters, 29 (1996), 111-117.
15. G. Zames and S. K. Mitter, A note on essential spectra and norms of mixed Hankel-Toeplitz operators, Systems & Control Letters, 10 (1988), 159-165.
16. K. Zhou and P. P. Khargonekar, On the weighted sensitivity minimization problem for delay systems, Systems & Control Letters, 8 (1987), 307-312.