Formulas for Hankel singular values and vectors for a class of input delay systems

Automatica

Volumn 35, Issue 2, 1999, Pages 201-215

  Ohta, Yoshito ^a,c   Kojima, Akira ^b,d  

^a OSAKA UNIVERSITY   (Japan)

^b TOKYO METROPOLITAN UNIVERSITY   (Japan)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^d WASEDA UNIVERSITY   (Japan)

Author keywords

Hankel operator; Input delay systems; Integral operators; Model reduction; Rational Approximation; Singular values

Indexed keywords

APPROXIMATION THEORY; MATHEMATICAL OPERATORS; TRANSFER FUNCTIONS; VECTORS;

HANKEL OPERATOR; INPUT DELAY SYSTEMS; INTEGRAL OPERATORS; RATIONAL APPROXIMATION;

DELAY CONTROL SYSTEMS;

EID: 0033075884     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0005-1098(98)00158-7     Document Type: Article

References (24)

1. Anderson, B. D. O., & Liu, Y. (1989). Controller reduction: Concepts and approaches. IEEE Trans. Automat. Control, AC-34(8), 802-812.
2. Banks, H. T., & Kappel, F. (1979). Spline approximations for lunctional differential equations. J. Differential Equations, 34, 496-522.
3. Chongsrid, K., & Hara, S. (1995). Hankel norm of sampled-data systems. IEEE Trans. Automat. Control, AC-40(11), 1939-1942.
4. Curtain, R. F. (1990). Robust stabilizability of normalized coprime factors: The infinite-dimensional case. Int. J. Control, 51(6), 1173-1190.
5. Dym, H., & Georgiou, T. T., & Smith, M. C. (1995). Explicit formulas for optimally robust controlers for delay systems. IEEE Trans. Automat. Control, AC-40(4), 656-669.
6. ∞ sensitivity minimization for delay systems. Systems Control Lett., 9, 17-24.
7. Glader, C., & Högnäs, G., Mäkilä, P. M., & Toivonen, H. T. (1991). Approximation of delay systems. Int. J. Control, 53(2), 369-390.
8. ∞-error bounds. Int. J. Control, 39(6), 1115-1193.
9. Glover, K., Curtain, R. F., & Partington, J. R. (1988). Realisation and approximation of linear infinite dimensional systems with error bounds. SIAM J. Control Optim., 26(4), 863-898.
10. Glover, K., Lam, J., & Partington, J. R. (1990). Rational approximation of a class of infinite-dimensional systems I: Singular values of Hankel operators. Math. Control Signals Systems, 3(4), 325-344.
11. Gohberg, I., Goldberg, S., & Kaashoek, M. A. (1990). Classes of linear operators (Vol. I). Operator theory: Advances and applications (Vol. 49). Basel: Birkhäuser.
12. Gu, G., Khargonekar, P. P., & Lee, E. B. (1992). Approximation of infinite-dimensional systems. IEEE Trans. Automat. Control, AC-34(6) 610-618.
13. Kung, S. Y., & Lin, D. W. (1981). Optimal Hankel norm model reductions: Multivariable systems. IEEE Trans. Automat. Control, AC-26(4), 832-852.
14. Lypchuk, T. A., Smith, M. C., & Tannenbaum, A. (1988). Weighted sensitivity minimization: General plants in H00 and rational weights. Linear Algebra Appl., 109, 71-90.
15. Moore, B. C. (1981). Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Trans. Automat. Control, AC-26(1), 17-32.
16. Ohta, Y., & Hwang, I. C. (1996). Hankel approximation of commensurate input delay systems. Proc. 35th Conf. on Decision and Control, Kobe (pp. 3167-3172).
17. Özbay, H. (1990). A simpler formula for the singular values of a certain Hankel operator. Systems Control Lett., 15(5), 381-390.
18. Pandolfi, L. (1993). An integral equation approach to the singular values of a system with distributed output delays. Systems Control Lett., 20, 447-454.
19. ∞ approximation and nuclearity of delay systems. Systems Control Lett., 10, 59-65.
20. Pernebo, L., & Silverman, L. M. (1982). Model reduction via balanced state space representation. IEEE Trans. Automat. Control, AC-27(4), 382-387.
21. Smith, M. C. (1989). Singular values and vectors of a class of Hankel operators. Systems Control Lett., 12, 301-308.
22. ∞ interpolation in systems with commensurate input lags. SIAM J. Control Optim. 511-526.
23. ∞ problem. Systems Control Lett., 29, 111-117.
24. Zhou, K., & Khargonekar, P. P. (1987). On the weighted sensitivity minimization problem for delay systems. Systems Control Lett., 8, 307-312.