Robust matrix script D sign U-stability analysis

International Journal of Robust and Nonlinear Control

Volumn 13, Issue 6, 2003, Pages 533-558

  Bachelier, Oliver ^a   Mehdi, D ^a  

^a UNIVERSITÉ DE POITIERS   (France)

Author keywords

LMI; Parameter dependent Lyapunov functions; Robust matrix root clustering; script D sign U stability

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS; MATHEMATICAL MODELS; PROBLEM SOLVING;

ROBUST MATRIX ROOT-CLUSTERING;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 0038291707     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/rnc.736     Document Type: Article

References (44)

1. Patton RJ, Liu GP. Robust control design via eigenstructure assignment, genetic algorithms and gradient-based optimisation. IEE Proceedings on Control Theory Applications 1994; 141(3):202-208.
2. Lam J, Tam HK. Regional pole placement with eigenstructure robustness. International Journal of Systems Science 1997; 28(5):507-515.
3. Bachelier O, Pardin B. Bounds for uncertain matrix root-clustering in a union of subregions. International Journal of Robust and Nonlinear Control 1999; 9(6):333-359.
4. Barmish BR, Kang HI. A survey of extreme point results for robustness of control systems. Automatica 1993; 29: 13-35.
5. Safonov MG. Stability margins for diagonally perturbed multivariable feedback systems. IEE Proceedings Part D 1982; 129:251-256.
6. Fan MKH, Tits AL, Doyle JC. Robustness in the presence of mixed parametric uncertainty and unmodeled dynamics. IEEE Transactions on Automatic Control 1991; 36(1):25-38.
7. Barmish BR. Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. Journal of Optimization Theory and Applications 1985; 46(4):399-408.
8. Bernussou J, Geromel JC, Peres PLD. A linear programming oriented procedure for quadratic stabilization of uncertain systems. Systems and Control Letters 1989; 13:65-72.
9. Becker G. Quadratic stability and performance of linear, parameter-dependent systems. Ph.D. Thesis, Mechanical Engineering, University of California, Berkeley, USA, 1993.
10. 2 guaranteed cost control for uncertain continuous-times linear systems. Systems and Control Letters 1992; 1:23-27.
11. Garcia G, Daafouz J, Bernussou J. Output feedback disk pole assignment for systems with positive real uncertainty. IEEE Transactions on Automatic Control 1996; 41(9):1385-1391.
12. Feron E, Apkarian P, Gahinet P. Analysis and synthesis of robust control systems via parameter dependent Lyapuonv functions. IEEE Transactions on Automatic Control 1996; 41:436-442.
13. Geromel JC, de Oliveira MC, Hsu L. LMI characterization of structural and robust stability. Linear Algebra and its Applications 1998; 285:69-80.
14. Chilai M, Gahinet P, Apkarian P. Robust pole placement in LMI regions. IEEE Transactions on Automatic Control 1999; 44(12):2257-2269.
15. Becker G, Packard A. Robust performance of linear, parametrically varying systems using parametrically-dependent linear dynamic feedback. Systems and Control Letters 1994; 23:205-215.
16. Packard A, Becker G. Quadratic stabilization of parametrically dependent linear systems using parametrically dependent linear feedback. Advances in Robust and Nonlinear Control Systems (ASME Winter Annual Meeting), 1992; DSC 43:29-36.
17. 2 norm control for 1pv systems with bounded parameter variation rates. International Journal of Robust and Nonlinear Control 1996; 6:983-998.
18. Peaucelle D, Arzelier D. Bachelier O, Bernussou J. A new robust D-stability condition for real convex polytopic uncertainty. Systems and Control Letters 2000: 40(1):21-30.
19. Bachelier O, Peaucelle D, Arzelier D, Bernussou J. A precise robust matrix root-clustering analysis with respect to polytopic uncertainty. In Proceedings of ACC, Chicago, USA, July 2000.
20. Tesi A, Vicino A. Robust stability of state-space models with structured uncertainty. IEEE Transactions on Automatic Control 1990; 35(2)191-195.
21. Patel RV, Toda M. Quantitative measures of robustness for multivariable systems. In Joint Automatic Control Conference, 1980.
22. Yedavalli RK, Liang Z. Reduced conservatism in stability robustness bounds by state transformation. IEEE Transactions on Automatic Control 1986; 31(9):863-866.
23. Luo JS, Johnson A, Van Den Bosch PPJ. Lyapunov stability robust analysis and robustness design for linear continuous-time systems. International Journal of Control 1995; 61(6):1233-1251.
24. Gardiner JD. Computation of stability bounds for state-space models with structured uncertainty. IEEE Transactions on Automatic Control 1997; 42(2):253-256.
25. Juang YT, Hong ZC, Wang YT. Lyapunov approach to robust pole assignment analysis. International Journal of Control 1989; 49:921-927.
26. Juang YT. Robust stability and robust pole assignment of linear systems with structured uncertainty. IEEE Transactions on Automatic Control 1991; 36(5):635-637.
27. Yedavalli RK. Robust root clustering for linear uncertain systems using generalized Lyapunov theory. Automatica 1993; 29(1):237-240.
28. Bakker W, Luo JS, Johnson A. Performance robustness bounds for linear systems to guarantee root-clustering in second order subrogions of the complex plane. In Proceedings of 32nd CDC, San Antonio, TX, USA, December 1993; 3467-3472.
29. Luo JS, Johnson A, Van Den Bosh PPJ. New Lyapunov robustness bounds for pole assignment in a specified region. In IFAC World Congress, vol. 2. Sydney, Australia, July 1993; 495-498.
30. Chouaib I, Pradin B. Parameters bounds for root clustering of uncertain matrices. International Journal of Systems Science 1995; 26(9):1601-1615.
31. Gutman S, Jury El. A general theory for matrix root-clustering in subrogions of the complex plane. IEEE Transactions on Automatic Control 1981; 26(4):853-863.
32. Ström T. On logarithmic norms. SIAM Journal on Numerical Analysis 1975; 12(5):741-753.
33. Ashokkumar CR, Yedavalli RK. Eigenstructure perturbation analysis in disjointed domains for linear uncertain systems. International Journal of Control 1997; 67(6):887-899.
34. Bachelier O. Commande des systèmes linéaires incertains: placement de pôles robuste en D-stabilité. Ph.D. Thesis, INSA, Toulouse-France, 1998.
35. Bachelier O, Pradin B. Robust matrix root-culstering in a union of Ω-subregions. International Journal of Systems Science 2001;32:467-477.
36. Peaucelle D. Formulation générique de problèmes en analyse et commande robuste par des fonctions de Lyapunov dependant de paramètres. Ph.D. Thesis, Université Paul Sabatier Toulouse III, Toulouse-France, July 2000.
37. ∞ design with pole placement constraints: an LMI approach. IEEE Transactions on Automatic Control 1996; 41(3):358-367.
38. Chilali M. Méthode LMI pour la synthèse multi-critère. Ph.D. Thesis, Université Paris IX-Dauphine, U.F.R. Mathématiques de la Décision, Paris-France, 1996.
39. Qui L, Bernhardsson B, Rantzer A, Davison EJ, Young PM, Doyle JC. A formula for computation of the real stability radius. Autamatica 1995; 31(6):879-890.
40. Gahinet P, Nemirovski A, Laub AJ, Chilali M. LMI Control Toolbox. The MathWorks, Inc.: Natick, MA, 1995.
41. Luo JS, Van den Bosch PPJ, Weiland S. New sufficient condition for robust root clustering of linear state space models with structured uncertainty. IEE Proceedings on Control Theory Applications 1996; 143(3):244-246.
42. Franklin GJ, Powell JD, Enami-Meimi A. Feedback Control of Dynamic Systems. Addison-Wesley: MA, 1986.
43. Liu GP, Patton RJ. Robust control design based on parametric eigenvalue assignment. International Journal of Systems Science 1998; 29(1):65-74.
44. Horn RA, Johnson CR. Topics in Matrix Analysis. Cambridge University Press: Cambridge, MA, 1991.