Remarks on control design with degree constraint

IEEE Transactions on Automatic Control

Volumn 51, Issue 7, 2006, Pages 1150-1156

  Georgiou, Tryphon T ^a   Lindquist, Anders ^b  

^a University of Minnesota   (United States)

^b ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

H control; Linear matrix inequalities (LMIs); McMillan degree constraint; Weighted entropy

Indexed keywords

FEEDBACK CONTROL; LINEAR EQUATIONS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS;

LINEAR MATRIX INEQUALITIES (LMIS); MCMILLAN DEGREE CONSTRAINT; WEIGHTED ENTROPY;

CONSTRAINT THEORY;

EID: 33746047115     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2006.878751     Document Type: Article

References (23)

1. 0 -inner matrix-valued functions," Russian Acad. Sci. Izv. Math., vol. 42, no. 1, pp. 1-26, 1994.
2. A. Blomqvist, "A convex optimization approach to complexity constrained analytic interpolation with applications to ARMA estimation and robust control," Ph.D. dissertation, Royal Inst. Technol., Stockholm, Sweden, 2005, TRITA-MAT-05-OS-01.
3. A. Blomqvist, A. Lindquist, and R. Nagamune, "Matrix-valued Nevanlinna-Pick interpolation with complexity constraint: An optimization approach," IEEE Trans. Autom. Control, vol. 48, no. 12, pp. 2172-2190, Dec. 2003.
4. C. Byrnes, T. T. Georgiou, and A. Lindquist, "A generalized entropy criterion for Nevanlinna-Pick interpolation: A convex optimization approach to certain problems in systems and control," IEEE Trans. Autom. Control, vol. 45, no. 6, pp. 822-839, Jun. 2001.
5. ∞ with a complexity constraint," Trans. Amer. Math. Soc., vol. 358, no. 3, pp. 965-987, Mar. 2006.
6. C. I. Byrnes and A. Lindquist, "On the duality between filtering and Nevanlinna-Pick interpolation," SIAM J. Control Optim., vol. 39, pp. 757-775, 2000.
7. C. I. Byrnes and A. Lindquist, K. Hashimoto, Y. Oishi, and Y. Yamamoto, Eds., "A convex optimization approach to generalized moment problems," in Control and Modeling of Complex Systems: Cybernetics in the 21st Century: Festschrift in Honor of Hidenori Kimura on the Occasion of his 60th Birthday. Boston, MA: Birkhauser, 2003, pp. 3-21.
8. ∞ control problems," IEEE Trans. Autom. Control, vol. 34, no. 8, pp. 831-847, Aug. 1989.
9. ∞-Control Theory. New York: Springer-Verlag, 1987.
10. D. McFarlane, D. Glover, and K. Robust, Controller Design Using Normalised Coprime Factor Plant Descriptions. Berlin, Germany: Springer Verlag, 1990.
11. ∞ control," Int. J. Robust Nonlinear Control, vol. 4, pp. 421-448, 1994.
12. T. T. Georgiou and A. Lindquist, "Kullback-Leibler approximation of spectral density functions," IEEE Trans. Inf. Theory, vol. 49, no. 11, pp. 2910-2917, Nov. 2003.
13. T. T. Georgiou, "Solution of the general moment problem via a one-parameter imbedding," IEEE Trans. Autom. Control, vol. 50, no. 6, pp. 811-826, Jun. 2005.
14. T. T. Georgiou, "Relative entropy and the multi-variable multi-dimensional moment problem," IEEE Trans. Inf. Theory, vol. 52, no. 3, pp. 1052-1066, Mar. 2006.
15. M. G. Krein and A. A. Nudel'man, The Markov Moment Problem and Extremal Problems. Providence, RI: AMS, 1977, p. 417.
16. ∞ control," SIAM Rev., vol. 35, pp. 652-654, 1993.
17. R. Nagamune, "Robust control with complexity constraint: A Nevanlinna-Pick interpolation approach," Ph.D. dissertation, Royal Inst. Technol., Stockholm, Sweden, 2002, TRITA-MAT-02-OS-10.
18. ∞," Trans. Amer. Math. Soc., vol. 127, pp. 179-203, 1967.
19. R. E. Skelton, T. Iwasaki, and K. Grigoriadis, A Unified Approach to Linear Control Design. New York: Taylor and Francis, 1997.
20. A. R. Tannenbaum, "Feedback stabilization of linear dynamical plants with uncertainty in the gain factor," Int. J. Control, vol. 32, pp. 1-16, 1980.
21. L. Y. Wang and G. Zames, "Lipschitz continuity of H-infinity interpolation," Syst. Control Lett., vol. 14, pp. 381-387, 1990.
22. G. Zames, "Feedback and optimal sensitivity: Model reference transformations, multiplicative seminorms, and approximate inverses," IEEE Trans. Autom. Control, vol. AC-26, no. 4, pp. 301-320, Apr. 1981.
23. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Upper Saddle River: Prentice-Hall, 1996.