Robust absolute stability and nonlinear state feedback stabilization based on polynomial Lur'e functions

Nonlinear Analysis, Theory, Methods and Applications

Volumn 70, Issue 5, 2009, Pages 1803-1812

  Montagner, V F ^a   Oliveira, R C L F ^b   Calliero, T R ^b   Borges, R A ^b   Peres, P L D ^b   Prieur, C ^c  

^a FEDERAL UNIVERSITY OF SANTA MARIA   (Brazil)

^b UNIVERSITY OF CAMPINAS   (Brazil)

^c UNIVERSITÉ DE TOULOUSE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

FEEDBACK; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; MATRIX ALGEBRA; NONLINEAR SYSTEMS; POLYNOMIAL APPROXIMATION; STABILIZATION; SYSTEM STABILITY; UNCERTAIN SYSTEMS; UNCERTAINTY ANALYSIS;

ABSOLUTE STABILITIES; ALGEBRAIC PROPERTIES; CONVEX CONDITIONS; EXISTING CONDITIONS; FEEDBACK STABILIZATIONS; INEQUALITY CONSTRAINTS; LINEAR MATRIXES; NON LINEARITIES; NONLINEAR STATES; NUMERICAL EXAMPLES; POSITIVE MATRIXES; ROBUST ABSOLUTE STABILITIES; ROBUST STABILITIES; UNCERTAIN PARAMETERS;

STATE FEEDBACK;

EID: 58149180361     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2008.02.081     Document Type: Article

References (30)

1. Albertini F., and D'Alessandro D. Asymptotic stability of continuous-time systems with saturation nonlinearities. Systems & Control Letters 29 3 (1996) 175-180
2. Arcak M., and Kokotovic P. Feasibility conditions for circle criterion designs. Systems & Control Letters 42 5 (2001) 405-412
3. Arcak M., Larsen M., and Kokotovic P. Circle and Popov criteria as tools for nonlinear feedback design. Automatica 39 4 (2003) 643-650
4. Barmish B.R. Necessary and sufficient conditions for quadratic stabilizability of an uncertain system. Journal of Optimization Theory and Applications 46 4 (1985) 399-408
5. Bliman P.-A. Absolute stability criteria with prescribed decay rate for finite-dimensional and delay systems. Automatica 38 11 (2002) 2015-2019
6. Bliman P.-A. An existence result for polynomial solutions of parameter-dependent LMIs. Systems & Control Letters 51 3-4 (2004) 165-169
7. P.-A. Bliman, R.C.L.F. Oliveira, V.F. Montagner, P.L.D. Peres, Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex, in: Proceedings of the 45th IEEE Conference on Decision and Control, San Diego, CA, December 2006, pp. 1486-1491
8. S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM Studies in Applied Mathematics, Philadelphia, PA, 1994
9. Chesi G., Garulli A., Tesi A., and Vicino A. Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach. IEEE Transactions on Automatic Control 50 3 (2005) 365-370
10. de Oliveira M.C., Geromel J.C., and Hsu L. A new absolute stability test for systems with state-dependent perturbations. International Journal of Robust and Nonlinear Control 12 14 (2002) 1209-1226
11. Gahinet P., Apkarian P., and Chilali M. Affine parameter-dependent Lyapunov functions and real parametric uncertainty. IEEE Transactions on Automatic Control 41 3 (1996) 436-442
12. Gahinet P., Nemirovskii A., Laub A.J., and Chilali M. LMI Control Toolbox User's Guide (1995), The Math Works Inc, Natick, MA
13. Geromel J.C., de Oliveira M.C., and Hsu L. LMI characterization of structural and robust stability. Linear Algebra and Its Applications 285 1-3 (1998) 69-80
14. Hardy G.H., Littlewood J.E., and Pólya G. Inequalities. 2 edition (1952), Cambridge University Press, Cambridge, UK
15. D. Henrion, D. Arzelier, D. Peaucelle, J.B. Lasserre, On parameter-dependent Lyapunov functions for robust stability of linear systems, in: Proceedings of the 43rd IEEE Conference on Decision and Control, Paradise Island, Bahamas, December 2004, pp. 887-892
16. Kaszkurewicz E., and Bhaya A. Robust stability and diagonal Liapunov functions. SIAM Journal on Matrix Analysis and Applications 14 (1993) 508-520
17. Kaszkurewicz E., and Bhaya A. Matrix Diagonal Stability in Systems and Computation (1999), Birkhäuser, Boston, MA
18. Khalil H.K. Nonlinear Systems (1996), Prentice Hall, Upper Saddle River, NJ
19. Oliveira R.C.L.F., and Peres P.L.D. Parameter-dependent LMIs in robust analysis: characterization of homogeneous polynomially parameter-dependent solutions via LMI relaxations. IEEE Transactions on Automatic Control 52 7 (2007) 1334-1340
20. Oliveira R.C.L.F., and Peres P.L.D. Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: Asymptotically exact LMI conditions. Linear Algebra and Its Applications 405 (2005) 209-228
21. Oliveira R.C.L.F., and Peres P.L.D. LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions. Systems & Control Letters 55 1 (2006) 52-61
22. Peaucelle D., Arzelier D., Bachelier O., and Bernussou J. A new robust D-stability condition for real convex polytopic uncertainty. Systems & Control Letters 40 1 (2000) 21-30
23. Persidskii S.K. Problem of absolute stability. Automation and Remote Control 12 (1969) 1889-1895
24. Popov V.-M. On the absolute stability of nonlinear controlled systems. Avtomatika i telemekhanika 8 (1961) 961-970
25. Ramos D.C.W., and Peres P.L.D. An LMI condition for the robust stability of uncertain continuous-time linear systems. IEEE Transactions on Automatic Control 47 4 (2002) 675-678
26. C.W. Scherer, Higher-order relaxations for robust LMI problems with verifications for exactness, in: Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, HI, USA, December 2003, pp. 4652-4657
27. Scherer C.W. Relaxations for robust linear matrix inequality problems with verifications for exactness. SIAM Journal on Matrix Analysis and Applications 27 2 (2005) 365-395
28. Scherer C.W., and Hol C.W.J. Matrix sum-of-squares relaxations for robust semi-definite programs. Mathematical Programming Series B 107 1-2 (2006) 189-211
29. Sturm J.F. Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones. Optimization Methods and Software 11-12 (1999) 625-653. http://sedumi.mcmaster.ca/ URL
30. Willems J.C. Least squares stationary optimal control and algebraic Riccati equation. IEEE Transactions on Automatic Control AC-16 6 (1971) 621-634