Approximate solutions to a weighted mixed-sensitivity H∞-control design for irrational transfer matrices

International Journal of Robust and Nonlinear Control

Volumn 6, Issue 5, 1996, Pages 399-411

  Curtain, R F ^a   Weiss, M ^a   Zhou, Y ^a  

^a UNIVERSITY OF GRONINGEN   (Netherlands)

Author keywords

Distributed parameter systems; Infinite dimensional systems; Model reduction; Multiplicative approximations; Weighted mixed sensitivity H control

Indexed keywords

APPROXIMATION THEORY; CONTROL SYSTEM SYNTHESIS; DELAY CONTROL SYSTEMS; DISTRIBUTED PARAMETER CONTROL SYSTEMS; ERRORS; MATRIX ALGEBRA; SYSTEM STABILITY; TRANSFER FUNCTIONS;

INFINITE DIMENSIONAL SYSTEMS; IRRATIONAL TRANSFER MATRIX; MODEL REDUCTION; MULTIPLICATIVE APPROXIMATION; WEIGHTED MIXED SENSITIVITY CONTROL;

OPTIMAL CONTROL SYSTEMS;

EID: 0030170493     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199606)6:5<399::AID-RNC220>3.0.CO;2-T     Document Type: Article

References (23)

1. Foias, C., A. Tannenbaum and G. Zames, 'Weighted sensitivity and minimization for delay systems', IEEE Trans. of Autom. Control, AC-31, 763-766 (1986).
2. ∞-optimal sensitivity problem for systems with delays', SIAM J. Control and OptimiZation, 25, 686-705 (1987).
3. Zhou, K., and P. P. Khargonekar, On the weighted sensitivity minimization problem for delay systems', Systems and Control Letters, 8, 307-312 (1987).
4. ∞ and rational weights', Linear Algebra and its Application, 109, 71-90 (1988).
5. ∞ optimal control design for a class of distributed parameter systems', Int. J. Control, 58, 739-782 (1993).
6. ∞-optimal control design for distributed plants', Int. J. Control, 54, 1291-1308 (1991).
7. Flamm, D. S., and H. Yang, 'Optimal mixed sensitivity for general distributed plants', Proc. IEEE Conf on Decision and Control, 1990.
8. ∞-control for Distributed Parameter Systems: A State Space Approach, Birkhäuser, Bosten, 1993.
9. Curtain, R. F., M. Weiss and Y. Zhou, 'Closed formulae for a parameteric-mixed-sensitivity problem for Pritchard-Salamon systems', Systems and Control Letters (to appear).
10. van Keulen, B., and F. Curtain, 'A styate-space approach to the mixed-sensitivity minimization problem for deelay systems', Control of Partial Differential Equations, Da Prato and Tubaro, eds., Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York, 1994, pp. 121-135.
11. ∞-control', manuscript.
12. ∞-control design for irrational transfer matrices', Tech. Report W-9416, Department of Mathematics, University of Groningen, The Netherlands, 1994.
13. Matson, J. B., J. Lam, B.D.O. Anderson and B. James, 'Multiplicative Hankel norm approximation of linear multivariable systems', Int. J. Control, 50, 129-167 (1993).
14. Lasieçka, and R. Triggiani, 'Differential and algebraic Riccati equations with applications to boundary/point control problems: continuous theory and approximation theory'. Lecture Notes in Control and Information Sciences, vol. 164, Springer Verlag, Berlin, 1991.
15. MATLAB, developed and copyrighted by the Math Works Inc. Natick. MA, 1994.
16. Curtain, C. F., and H. Zwart, An Introduction to Infinite-dimensional Linear Systems Theory, Springer Verlag, New York, 1995.
17. Vidyasager, M., Control System Synthesis: A Factori:ation Approach, MIT Press, Boston, 1985.
18. Rudin, W., Real and Complex Analysis, 2nd edition, McGraw Hill, New York, 1974.
19. Logemann, H., On the Nyquist criterion and the brobust stabilization for infinite-dimensional systems', Proc. Int. Symposium MTNS-89, Vol. 2, M. A. Kaashoek, J. H. van Schuppen and A. C. M. Ran, eds, Birkhäuser, Boston, 1990-638.
20. Curtain, C. F., 'A synthesis of time and frequency domain methods for the control of infinite-dimensional systems: a system theoretic approach', Control and Estimation in Distributed Parameter Systems, Frontier in Applied Mathematics, H. T. Banks, ed., SIAM, Philadaphia, 1992, pp. 171-224.
21. ∞ controllers for unstable distributed plants', Proceedings of 32nd IEEE Conference on Decision and Control, San Antonio, TX, December 1993, pp. 1170-1175.
22. Curtain, R. F., and G. Weiss, 'Well-posed ness of triples of operators (in the sense of linear systems theory', Proc. 4th Int. Conf. on Control of Distributed Parameter Systems, Vorau, Italy, 1988, Birkhäuser-Verlag, Basel, also Int. Series of Numerical Math., 91, 41-59 (1989).
23. Curtain, R. F., and G. Weiss, 'Well-posed ness of triples of operators (in the sense of linear systems theory', Proc. 4th Int. Conf. on Control of Distributed Parameter Systems, Vorau, Italy, 1988, Birkhäuser-Verlag, Basel, also Int. Series of Numerical Math., 91, 41-59 (1989).