Solving quadratic distance problems: An LMI-based approach

IEEE Transactions on Automatic Control

Volumn 48, Issue 2, 2003, Pages 200-212

  Chesi, Graziano ^a   Garulli, Andrea ^a   Tesi, Alberto ^b   Vicino, Antonio ^a  

^a UNIVERSITY OF SIENA   (Italy)

^b UNIVERSITY OF FLORENCE   (Italy)

Author keywords

Distance problems; Homogeneous forms; Linear matrix inequalities (LMIs); Optimization

Indexed keywords

APPROXIMATION THEORY; COMPUTER SIMULATION; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PROBLEM SOLVING;

LINEAR MATRIX INEQUALITIES (LMI);

LINEAR CONTROL SYSTEMS;

EID: 0037291895     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2002.808465     Document Type: Article

References (32)

1. S. P. Bhattacharyya, H. Chapellat, and L. H. Keel, Robust Control: The Parametric Approach. Upper Saddle River, NJ: Prentice-Hall, 1995.
2. R. Genesio, M. Tartaglia, and A. Vicino, "On the estimation of asymptotic stability regions: State of the art and new proposals," IEEE Trans. Automat. Contr., vol. AC-30, pp. 747-755, Aug. 1985.
3. Z. Zhang, "Determining the epipolar geometry and its uncertainty-A review," Int. J. Comput. Vision, vol. 27, no. 2, pp. 161-195, 1998.
4. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM, 1994.
5. A. Megretski and A. Rantzer, "System analysis via integral quadratic constraints," IEEE Trans. Automat. Contr., vol. 42, pp. 819-830, 1997.
6. G. Chesi, R. Genesio, and A. Tesi, "Optimal ellipsoidal stability domain estimates for odd polynomial systems," in Proc. 36th IEEE Conf. Decision Control, San Diego, CA, 1997, pp. 3528-3529.
7. G. Chesi, A. Tesi, A. Vicino, and R. Genesio, "A convex approach to a class of minimum norm problems," in Robustness in Identification and Control, A. Garulli, A. Tesi, and A. Vicino, Eds. London, U.K.: Springer-Verlag, 1999, pp. 359-372.
8. G. Chesi, A. Garulli, A. Vicino, and R. Cipolla, "Estimating the fundamental matrix via constrained least squares: A convex approach," IEEE Trans. Pattern Anal. Machine Intell., vol. 24, pp. 397-401, 2002.
9. G. Chesi, A. Tesi, A. Vicino, and R. Genesio, "An LMI approach to constrained optimization with homogeneous forms," Syst. Control Lett., vol. 42, pp. 11-19, 2001.
10. G. Hardy, J. E. Littlewood, and G. Pólya, Inequalities: Second Edition. Cambridge, U.K.: Cambridge Univ. Press, 1988.
11. N. Z. Shor, "Class of global minimum bounds of polynomial functions" (in Russian), Cybernetics, vol. 23, pp. 731-734, 1987.
12. P. A. Parrilo, "Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization," Ph.D. dissertation, California Inst. Technol., Pasadena, CA, 2000.
13. Y. Nesterov, "Squared functional systems and optimization problems," in High Performance Optimization, H. Frenk, K. Roos, T. Terlaky, and S. Shang, Eds. Norwell, MA: Kluwer, 2000.
14. Y. Genin, Y. Hachez, Y. Nesterov, and P. Van Dooren. (2001) Optimization problems over positive pseudo-polynomial matrices. [Online]. Available: http://www.auto.ucl.ac.be/̃vdooren
15. A. Rantzer and P. A. Parrilo, "On convexity in stabilization of nonlinear systems," in Proc. 39th IEEE Conf. Decision Control, Sydney, Australia, 2000, pp. 2942-2945.
16. B. Tibken, "Estimation of the domain of attraction for polynomial systems via LMI's," in Proc. 39th IEEE Conf. Decision. Control, Sydney, Australia, 2000, pp. 3860-3864.
17. D. Hershkowitz, "Recent directions in matrix stability," Linear Alg. Appl., vol. 171, pp. 161-186, 1992.
18. H. K. Khalil, Nonlinear Systems. New York: McMillan, 1992.
19. ∞ -control," IEEE Trans. Automat. Contr., vol. 37, pp. 770-784, June 1992.
20. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "A convex approach to the characterization of the frequency response of ellipsoidal plants," Automatica, vol. 38, pp. 249-259, 2002.
21. G. Chesi, "New convexification techniques and their applications to the analysis of dynamic systems and vision problems," Ph.D. dissertation, Università di Bologna, Bologna, Italy, 2001.
22. H. K. Khalil, Nonlinear Systems. New York: McMillan, 1992.
23. E. J. Davison and E. M. Kurak, "A computational method for determining quadratic Lyapunov functions for nonlinear systems," Automatica, vol. 7, pp. 627-636, 1971.
24. A. N. Michel, N. R. Sarabudla, and R. K. Miller, "Stability analysis of complex dynamical systems. Some computational methods," Circuits Syst. Signal Processing, vol. 1, pp. 561-573, 1982.
25. H. D. Chiang and J. S. Thorp, "Stability regions of nonlinear dynamical systems: A constructive methodology," IEEE Trans. Automat. Contr., vol. 34, pp. 1229-1241, 1989.
26. A. T. Fuller, "Conditions for a matrix to have only characteristic roots with negative real parts," J. Math. Anal. Appl., vol. 23, pp. 71-98, Dec. 1968.
27. A. Tesi and A. Vicino, "Robust stability of state space models with structured uncertainties," IEEE Trans. Automat. Contr., vol. 35, pp. 191-195, Feb. 1990.
28. A. Vicino, A. Tesi, and M. Milanese, "Computation of nonconservative stability perturbation bounds for systems with nonlinearly correlated uncertainties," IEEE Trans. Automat. Contr., vol. 35, pp. 835-841, July 1990.
29. O. Faugeras, Three-Dimensional Computer Vision: A Geometric Viewpoint. Cambridge, MA: MIT Press, 1993.
30. Y. Nesterov and A. Nemirovsky, Interior Point Polynomial Methods in Convex Programming: Theory and Applications. Philadelphia, PA: SIAM, 1993.
31. T. S. Motzkin, "The arithmetic-geometric inequality," in Inequalities, O. Shisha, Ed. New York: Academic, 1967.
32. S. Basu, "A constructive algorithm for 2-D spectral factorization with rational spectral factors," IEEE Trans. Circuits Syst., vol. 47, pp. 1309-1318, Sept. 2000.