Bounding the parameters of linear systems with stability constraints

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 2152-2157

  Cerone, V ^a   Piga, D ^a   Regruto, D ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

LMI relaxation; Set membership identification; Stability constraints

Indexed keywords

LINEAR SYSTEMS; RELAXATION PROCESSES; UNCERTAINTY ANALYSIS;

FEASIBLE PARAMETER SETS; GEOMETRICAL STRUCTURE; INPUT-OUTPUT MEASUREMENTS; LMI RELAXATION; NONCONVEX OPTIMIZATION PROBLEM; PARAMETERS UNCERTAINTIES; SET-MEMBERSHIP IDENTIFICATION; STABILITY CONSTRAINTS;

SYSTEM STABILITY;

EID: 77957783217     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2010.5531340     Document Type: Conference Paper

References (22)

1. L. Ljung, System Identification, Theory for the User. Upper Saddle River: Prentince Hall, 1999.
2. T. Söderström and P. Stoica, "On the stability of dynamic models obtained by least-squares identification," IEEE Trans. Automatic Control, vol. 26, no. 2, pp. 575-577, 1981.
3. P. Regalia and P. Stoica, "Stability of multivariable least-squares models," IEEE Signal. Processing Letters, vol. 2, no. 10, pp. 195-196, 1995.
4. J. Tugnait and C. Tontiruttananon, "Identification of linear systems via spectral analysis given time-domain data: Consistency, reduced-order approximation, and performance analysis," IEEE Trans. Automatic Control, vol. 43, no. 10, pp. 1354-1373, 1998. (Pubitemid 128737409)
5. P. Janakiraman and A. Bhattacharyya, "Stable output error identification scheme using periodic excitation signals," in Proc. of IEEE International Symposium on Circuits and Systems, vol. 5, 1999, pp. 539-542.
6. G. D. Nicolao and G. Pillonetto, "A new kernel-based approach for system identification," in Proc. of the American Control Conference, 2008, pp. 4510-4516.
7. S. Lacy and D. Bernstein, "Subspace identification with guaranteed stability using constrained optimization," IEEE Trans. Automatic Control, vol. 48, no. 7, pp. 1259-1263, 2003.
8. M. Milanese and A. Vicino, "Optimal estimation theory for dynamic sistems with set membership uncertainty: an overview," Automatica, vol. 27(6), pp. 997-1009, 1991.
9. E. Walter and H. Piet-Lahanier, "Estimation of parameter bounds from bounded-error data: a survey," Mathematics and Computers in simulation, vol. 32, pp. 449-468, 1990.
10. M. Milanese, J. Norton, H. Piet-Lahanier, and E. Walter, Eds., Bounding approaches to system identification. New York: Plenum Press, 1996.
11. J. Norton (Ed.), "Special issue on bounded-error estimation," Int. J. of Adapt. Control & Sign. Proces., vol. 8, no. 1, 1994.
12. -, "Special issue on bounded-error estimation," Int. J. of Adapt. Control & Sign. Proces., vol. 9, no. 1, 1995.
13. S. Veres and J. Norton, "Parameter-bounding algorithms for linear errors in variables models," in Proc. of IFAC/IFORS Symposium on Identification and System Parameter Estimation, 1991, pp. 1038-1043.
14. V. Cerone, "Parameter bounds for armax models from records with bounded errors in variables," Int. J. Control, vol. 57, no. 1, pp. 225-235, 1993.
15. -, "Feasible parameter set for linear models with bounded errors in all variable," Automatica, vol. 29, no. 6, pp. 1551-1555, 1993.
16. E. Jury, The theory and application of Z-transform method. New York: Wiley, 1964.
17. V. Cerone, D. Piga, and D. Regruto, "Bounding the parameters of linear systems with stability constraints," DAUIN Internal Report 2010/03/10, 2010.
18. M. Laurent, "Sums of squares, moment matrices and optimization over polynomials," Emerging Applications of Algebraic Geometry, Vol. 149 of IMA Volumes in Mathematics and its Applications, M. Putinar and S. Sullivant (eds.), pp. 157-270, 2009.
19. P. Parrillo, "Semidefinite programming relaxations for semialgebraic problems," Mathematical Programming, vol. 96, pp. 293-320, 2003.
20. J. B. Lasserre, "Global optimization with polynomials and the problem of moments," SIAM Journal on Optimization, vol. 11, pp. 796-817, 2001.
21. D. Henrion and J. B. Lasserre, "Gloptipoly: Global optimization over polynomials with Matlab and SeDuMi," ACM Transactions Math. Soft, vol. 29, pp. 165-194, 2003. (Pubitemid 40001449)
22. J. F. Sturm, "Using SeDuMi 1.02, a MATLAB Toolbox for optimization over symmetric cones," Optim. Methods Software, vol. 11, no. 12, pp. 625-653, 1999.