Extension of Parrott's theorem to nondefinite scalings

IEEE Transactions on Automatic Control

Volumn 45, Issue 5, 2000, Pages 937-940

  D'Andrea, Raffaello ^a  

^a Cornell University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

LINEAR SYSTEMS; MATHEMATICAL MODELS; MATRIX ALGEBRA; OPTIMAL CONTROL SYSTEMS; THEOREM PROVING;

LINEAR MATRIX INEQUALITY; PARROTT THEOREM;

CONTROL SYSTEM SYNTHESIS;

EID: 0034187410     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.855555     Document Type: Article

References (15)

1. C. Davis, W. M. Kahan, and H. F. Weinberger, "Norm-preserving dilations and their applications to optimal error bounds," SIAM J. Numerical Anal., vol. 19, no. 3, pp. 445-469, 1982.
2. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.
3. S. Parrott," On a quotient norm and the Sz.-Nagy-Foiaslifting theorem," J. Functional Anal., vol. 30, pp. 311-328, 1978.
4. A. Packard, "Gain scheduling via linear fractional transformations," Syst. Contr. Lett., vol. 22, no. 2, pp. 79-92, 1994.
5. A. Packard, K. Zhou, P. Pandey, J. Leonhardson, and G. Balas, "Optimal constant I/O similarity scalings for full information and state feedback control problems," Syst. Contr. Lett., vol. 19, pp. 271-280, 1992.
6. S. P. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
7. P. Gahinet and P. Apkarian, "A linear matrix inequality approach to H-infinity control," Int. J. Robust and Nonlinear Contr., vol. 4, pp. 421-448, 1994.
8. R. D'Andrea, "A linear matrix inequality approach to decentralized control of distributed parameter systems," in Proc. American Control Conf., 1998, pp. 1350-1354.
9. 2 synthesis for multidimensional systems," in Proc. IEEE Conf. Decision Control, 1998, pp. 1883-1888.
10. A. Rantzer, "On the Kalman-Yakubovich-Popov lemma," Syst. Contr. Lett., vol. 28, no. 1, pp. 7-10, 1996.
11. G. E. Dullerud, R. D'Andrea, and S. Lall, "Control of spatially varying distributed systems," in Proc. IEEE Conf. Decision Control, 1998, pp. 1889-1893.
12. I. Gohberg, M. A. Kaashoek, and H. J. Woerdeman, "The band method for positive and contractive extension problems," J. Operator Theory, vol. 22, pp. 109-155, 1989.
13. V. Ionescu and C. Oara, "The four-block Nehari problem: A generalized Popov-Yakubovich-type approach," IMA J. Math. Contr. Information, vol. 13, pp. 173-194, 1996.
14. M. Marcus and H. Minc, A Survey of Matrix Theory and Matrix Inequalities. New York: Dover, 1992.
15. R. D'Andrea and C. Beck, "Temporal discretization of spatially distributed systems," in Proc. IEEE Conf. Decision and Control, 1999, pp. 197-202.