Gain-scheduled controllers for linear parameter-varying systems with saturating actuators: LMI-based design

Proceedings of the American Control Conference

Volumn , Issue , 2007, Pages 6067-6072

  Montagner, Vinícius F ^a   Oliveira, Ricardo C L F ^b   Peres, Pedro L D ^b   Tarbouriech, Sophie ^c   Queinnec, Isabelle ^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

ACTUATORS; ASYMPTOTIC STABILITY; CONTROL THEORY; EIGENVALUES AND EIGENFUNCTIONS; LINEAR CONTROL SYSTEMS; LINEAR MATRIX INEQUALITIES; LINEAR SYSTEMS; MATRIX ALGEBRA; MILITARY DATA PROCESSING; PARAMETER ESTIMATION; STATE FEEDBACK; STATE SPACE METHODS; TRAJECTORIES;

(001) PARAMETER; (I ,J) CONDITIONS; ARBITRARY DEGREES; CLOSED-LOOP SYSTEMS; DOMAIN OF ATTRACTION; GAIN SCHEDULED (GS) CONTROLLERS; INITIAL CONDITIONS; LEVEL OF RELAXATION; LINEAR MATRICES; LINEAR PARAMETER-VARYING (LPV) SYSTEMS; NUMERICAL EXAMPLES; POLYTOPE; SATURATING ACTUATORS; STATE FEEDBACK GAIN; STATE SPACES; SUFFICIENT CONDITIONS (SC);

FEEDBACK;

EID: 46449122160     PISSN: 07431619     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/ACC.2007.4282551     Document Type: Conference Paper

References (40)

1. S. Tarbouriech, G. Garcia, and A. H. Glattfelder, Eds., Advanced Strategies in Control Systems with Input and Output Constraints, ser. Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer-Verlag, 2007, vol. 346.
2. D. S. Bernstein and A. N. Michel, "A chronological bibliography on saturating actuators," Int. J. Robust Nonlinear Contr., vol. 5, no. 5, pp. 375-380, 1995.
3. T. Hu and Z. Lin, Control Systems with Actuator Saturation: Analysis and Design. Boston, MA: Birkhäuser, 2001.
4. A. Saberi, Z. Lin, and A. R. Teel, "Control of linear systems with saturating actuators," IEEE Trans. Automat. Contr., vol. 41, no. 3, pp. 368-378, 1996.
5. S. Tarbouriech and G. Garcia, Eds., Control of Uncertain Systems with Bounded Inputs, ser. Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer-Verlag, 1997, vol. 227.
6. J. M. Gomes da Silva Jr. and S. Tarbouriech, "Local stabilization of discrete-time linear systems with saturating controls: An LMI-based approach," IEEE Trans. Automat. Contr., vol. 46, no. 1, pp. 119-125, 2001.
7. S. Tarbouriech, G. Garcia, and J. M. Gomes da Silva Jr., "Robust stability of uncertain polytopic linear time-delay systems with saturating inputs: an LMI approach," Comp. & Elect. Eng., vol. 28, no. 3, pp. 157-169, 2002.
8. H. Hu, Z. Lin, and B. M. Chen, "An analysis and design method for linear systems subject to actuator saturation and disturbance," Automatica, vol. 38, no. 2, pp. 351-359, 2002.
9. D. Henrion, G. Garcia, and S. Tarbouriech, "Piecewise-linear robust control of systems with input constraints," European J. Contr., vol. 5, no. 1, pp. 157-166, 1999.
10. R. Goebel, A. R. Teel, T. Hu, and Z. Lin, "Conjugate convex Lyapunov functions for dual linear differential inclusions," IEEE Trans. Automat. Contr., vol. 51, no. 4, pp. 661-666, 2006.
11. H. K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Prentice Hall, 1996.
12. J. M. Gomes da Silva Jr. and S. Tarbouriech, "Polyhedral regions of local stability for linear discrete-time systems with saturating controls," IEEE Trans. Automat. Contr., vol. 44, no. 11, pp. 2081-2085, 1999.
13. Y. Cao, Z. Lin, and D. G. Ward, "An antiwindup approach to enlarging domain of attraction for linear systems subject to actuator saturation," IEEE Trans. Automat. Contr., vol. 47, no. 1, pp. 140-145, 2002.
14. J. M. Gomes da Silva Jr. and S. Tarbouriech, "Antiwindup design with guaranteed regions of stability: An LMI-based approach," IEEE Trans. Automat. Contr., vol. 50, no. 1, pp. 106-111, 2005.
15. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Philadelphia, PA: SIAM Studies in Applied Mathematics, 1994.
16. P. Gahinet, A. Nemirovskii, A. J. Laub, and M. Chilali, LMI Control Toolbox User's Guide. The Math Works Inc., Natick, MA, 1995.
17. J. F. Sturm, "Using SeDuMi 1.02, a MATLAB toolbox for optimization over symmetric cones," Optimization Methods and Software, vol. 11-12, pp. 625-653, 1999, URL: http://sedumi.mcmaster.ca/.
18. P. Apkarian and H. D. Tuan, "Parametrized LMIs in control theory," SIAM J. Control Optim., vol. 38, no. 4, pp. 1241-1264, 2000.
19. G. Becker and A. Packard, "Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback," Syst. Contr. Lett., vol. 23, no. 3, pp. 205-215, 1994.
20. P.-A. Bliman, "Stabilization of LPV systems," in Proc. 42nd IEEE Conf. Decision Contr., Maui, Hawaii, 2003, pp. 6103-6108.
21. D. J. Leith and W. E. Leithead, "Survey of gain-scheduling analysis and design," Int. J. Contr., vol. 73, no. 11, pp. 1001-1025, 2000.
22. W. J. Rugh and J. S. Shamma, "Research on gain scheduling," Automatica, vol. 36, no. 10, pp. 1401-1425, 2000.
23. C. W. Scherer, "LPV control and full block multipliers," Automatica, vol. 37, no. 3, pp. 361-375, 2001.
24. G. Scorletti and L. El Ghaoui, "Improved LMI conditions for gain scheduling and related control problems," Int. J. Robust Nonlinear Contr., vol. 8, no. 10, pp. 845-877, 1998.
25. ∞ control of uncertain linear systems via parameter-dependent Lyapunov functions," in Proc. 39th IEEE Conf. Decision Contr., Sydney, Australia, 2000, pp. 3194-3199.
26. 2 analysis and control of linear parameter-dependent systems," IEE Proc. - Contr. Theory and Appl., vol. 150, no. 5, pp. 501-508, 2003.
27. ∞ linear parameter-varying state feedback control," IEE Proc. - Contr. Theory and Appl., vol. 152, no. 2, pp. 195-201, 2005.
28. 2 gain scheduled state feedback for LPV system with new LMI formulation," IEE Proc. - Contr. Theory and Appl., vol. 152, no. 6, pp. 693-697, 2005.
29. P.-A. Bliman, "An existence result for polynomial solutions of parameter-dependent LMIs," Syst. Contr. Lett., vol. 51, no. 3-4, pp. 165-169, 2004.
30. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Polynomially parameter-dependent Lyapunov functions for robust stability of polytopic systems: An LMI approach," IEEE Trans. Automat. Contr., vol. 50, no. 3, pp. 365-370, 2005.
31. R. C. L. F. Oliveira and P. L. D. Peres, "LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions," Syst. Contr. Lett., vol. 55, no. 1, pp. 52-61, 2006.
32. G. H. Hardy, J. E. Littlewood, and G. Pólya, Inequalities, 2nd ed. Cambridge, UK: Cambridge University Press, 1952.
33. C. W. Scherer, "Higher-order relaxations for robust LMI problems with verifications for exactness," in Proc. 42nd IEEE Conf. Decision Contr., Maui, HI, USA, 2003, pp. 4652-4657.
34. _, "Relaxations for robust linear matrix inequality problems with verifications for exactness," SIAM J. Matrix Anal. Appl., vol. 27, no. 2, pp. 365-395, 2005.
35. R. C. L. F. Oliveira and P. L. D. Peres, "Stability of polytopes of matrices via affine parameter-dependent Lyapunov functions: Asymptotically exact LMI conditions," Lin. Alg. Appl., vol. 405, pp. 209-228, 2005.
36. V. F. Montagner, P. L. D. Peres, S. Tarbouriech, and I. Queinnec, "Improved estimation of stability regions for uncertain linear systems with saturating actuators: an LMI-based approach," in Proc. 45th IEEE Conf. Decision Contr., San Diego, CA, 2006, pp. 5429-5434.
37. P.-A. Bliman, R. C. L. F. Oliveira, V. F. Montagner, and P. L. D. Peres, "Existence of homogeneous polynomial solutions for parameter-dependent linear matrix inequalities with parameters in the simplex," in Proc. 45th IEEE Conf. Decision Contr., San Diego, CA, 2006, pp. 1486-1491.
38. ∞ performance of linear time-varying systems in polytopic domains," Int. J. Contr., vol. 77, no. 15, pp. 1343-1352, 2004.
39. G. Chesi, A. Garulli, A. Tesi, and A. Vicino, "Robust stability of time-varying polytopic systems via parameter-dependent homogeneous Lyapunov functions," Automatica, vol. 43, no. 2, pp. 309-316, 2007.
40. J. C. Geromel and P. Colaneri, "Robust stability of time varying polytopic systems," Syst. Contr. Lett., vol. 55, no. 1, pp. 81-85, 2006.