An exact stability analysis test for single-parameter polynomially- dependent linear systems

Proceedings of the IEEE Conference on Decision and Control

Volumn 2, Issue , 2004, Pages 1337-1340

  Tsiotras, P ^a   Bliman, P A ^b  

^a Georgia Institute of Technology   (United States)

^b INRIA ROCQUENCOURT   (France)

Author keywords

[No Author keywords available]

Indexed keywords

LYAPUNOV METHODS; MATHEMATICAL MODELS; MATRIX ALGEBRA; PARAMETER ESTIMATION; POLYNOMIALS; PROBLEM ORIENTED LANGUAGES; PROBLEM SOLVING; THEOREM PROVING;

LINEAR MATRIX INEQUALITIES (LMI); LYAPUNOV FUNCTIONS; POLYNOMIAL MATRICES; STABILITY ANALYSIS;

LINEAR SYSTEMS;

EID: 14344254972     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/cdc.2004.1430228     Document Type: Conference Paper

References (20)

1. S. Bialas, "A necessary and sufficient condition for stability of convex combinations of stable polynomials and matrices," Bull. Polish Acad. Sci. Tech. Sci., vol. 33, no. 9-10, pp. 473-480, 1985.
2. M. Fu and B. R. Barmish, "Maximal unidirectional perturbation bounds for stability of polynomials and matrices," Systems and Control Letters, vol. 11, pp. 173-179, 1988.
3. L. Saydy, A. L. Tits, and E. H. Abed, "Robust stability of linear systems relative to guarded domains," in Proceedings of the 27th IEEE Conference on Decision and Control, 1988, pp. 544-551, Austin, TX.
4. _, "Guardian maps and the generalized stability of parametrized families of matrices and polynomials," Mathematics of Control, Signals and Systems, vol. 3, pp. 345-371, 1990.
5. B. R. Barmish, New Tools for Robustness of Linear Systems. Macmillan Publishing Company, 1994.
6. S. Rern, P. T. Kabamba, and D. S. Bernstein, "Guardian map approach to robust stability of linear systems with constant real parameter uncertainty," IEEE Transactions on Automatic Control, vol. 39, pp. 162-164, 1994.
7. E. Feron, P. Apkarian, and P. Cabinet, "Analysis and synthesis of robust control systems via parameter-dependent Lyapunov functions," IEEE Transactions on Automatic Control, vol. 41, no. 7, pp. 1041-1046, 1996.
8. P. Cabinet, P. Apkarian, and M. Chilali, "Affine parameter-dependent Lyapunov functions and real parametric uncertainty," IEEE Transactions on Automatic Control, vol. 41, no. 3, pp. 436-442, 1996.
9. A. Trofino, "Parameter depedent Lyapunov functions for a class of uncertain linear systems: an LMI approach," in Proceedings of the 38th IEEE Conference on Decision and Control, 1999, pp. 2341-2346, Phoenix, AZ.
10. D. Ramos and P. Peres, "An LMI condition for the robust stability of uncertain continuous-time linear systems," IEEE Transactions on Automatic Control, vol. 47, no. 4, pp. 675-678, 2002.
11. P. A. Bliman, "A convex approach to robust stability for linear systems with uncertain scalar parameters," SIAM Journal on Control and Optimization, vol. 42, no. 6, pp. 2016-2042, 2004.
12. P.-A. Bliman, "An existence result for polynomial solutions of parameter-dependent LMIs," Systems & Control Letters, vol. 51, no. 3-4, pp. 165-169, 2004.
13. P. A. Bliman, "Nonconservative LMI approach to robust stability for systems with uncertain scalar parameters," in Proceedings of the IEEE 41st Conference on Decision and Control, Dec. 2002, pp. 305-310, Las Vegas, NV.
14. X. Zhang, P. Tsiotras, and T. Iwasaki, "Parameter-dependent Lyapunov functions for stability analysis of LTI parameter dependent systems," in 42nd IEEE Confernce on Decision and Control, 2003, pp. 5168-5173, Maui, HW.
15. X. Zhang, "Parameter-dependent Lyapunov functions and stability analysis of linear parameter-dependent dynamical systems," Ph.D. dissertation, School of Aerospace Engineering, Georgia Institute of Technology, Atlanta, Georgia, October 2003.
16. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Robust stability of polytopic systems via polynomially parameter-dependent Lyapunov functions," in Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, pp. 4670-4675, Maui, HW.
17. G. Chesi, "Robust analysis of linear systems affected by time-invariant hypercubic parameter uncertainty," in Proceedings of the 42nd IEEE Conference on Decision and Control, 2003, pp. 5019-5024, Maui, HW.
18. T. Iwasaki, G. Meinsma, and M. Fu, "Generalized S-procedure and finite frequency KYP lemma," Mathematical Problems in Engineering, vol. 6, pp. 305-320, 2000.
19. T. Iwasaki and G. Shibata, "LPV system analysis via quadratic separator for uncertain implicit systems," IEEE Transactions on Automatic Control, vol. 46, no. 8, pp. 1195-1208, 2001.
20. X. Zhang, A. Lanzon, and P. Tsiotras, "On robust stability of LTI parameter dependent systems," in 10th Mediterranean Conference on Control and Automation, July 2002, Lisbon, Portugal.