Improved lmi conditions for gain scheduling and related control problems

International Journal of Robust and Nonlinear Control

Volumn 8, Issue 10, 1998, Pages 845-877

  Scorletti, Gérard ^a,b   El Ghaoui, Laurent ^b  

^a LSS   (France)

^b ENSTA PARISTECH   (France)

Author keywords

Anti windup control; Gain scheduling; Linear matrix inequality

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; CONTROL SYSTEM SYNTHESIS; LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; STATE SPACE METHODS; SYSTEM STABILITY; TIME VARYING CONTROL SYSTEMS;

GAIN SCHEDULING; LINEAR MATRIX INEQUALITY (LMI);

GAIN CONTROL;

EID: 0032141807     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199808)8:10<845::AID-RNC350>3.0.CO;2-I     Document Type: Article

References (52)

1. Doyle, J., A. Packard and K. Zhou, 'Review of LFTs, LMI's and μ, Proc. IEEE Conf. on Decision and Control, volume 2, Brighton, UK, December 1991, pp. 1227-1232.
2. Packard, A., K. Zhou, P. Pandey and G. Becker, 'A collection of robust control problems leading to LMI's', Proc. IEEE Conf. on Decision and Control, volume 2, Brighton, UK. December 1991, pp. 1245-1250.
3. Lu, W. M., K. Zhou and J. C. Doyle, 'Stabilization of LFT systems', Proc. IEEE Conf. on Decision and Control, Brighton, UK, December 1991, pp. 1238-1244.
4. Packard, A., 'Gain scheduling via linear fractional transformations', Syst. Control Letters, 22(2), 79-92 (1994).
5. ∞ controllers', IEEE Trans. Automat Control, 40(5), 853-864 (1995).
6. ∞gain-scheduling', Proc. American Control Conf., San Francisco, CA, May 1993, pp 328-333.
7. Becker, G., A. Packard, D. Philbrick and G. Balas, 'Control of parametrically dependent linear systems: a single quadratic Lyapunov approach', 1993 American Control Conference, volume 3, June 1993, pp. 2795-2799.
8. ∞ control of linear parameter-varying systems', Proc. American Control Conf., Baltimore, Maryland, June 1994, pp. 856-860.
9. Becker, G. and A. Packard, 'Robust performance of linear parametrically varying systems using parametrically-dependent linear feedback', Syst. Control Letters, 23(3), 205-215 (1994).
10. Helmersson, A., 'μ synthesis and LFT gain scheduling with mixed uncertainties', Proc. European Control Conf, Roma, Italy, 1995, pp. 153-158.
11. Helmersson, A., 'Methods for robust gain scheduling', Ph.D. Thesis, Linköping University, November 1995.
12. 2 norm control for LPV system with bounded parameter variation rates', Proc. American Control Conf, Seattle, Washington, June 1995, pp. 2379-2383.
13. Fromion, V., S. Monaco and D. Normand-Cyrot, 'Robustness and stability of LPV plants through frozen system analysis', Int. J. Robust and Nonlinear Control, 6, 235-248 (1996).
14. Willems, J. C., 'Qualitative behavior of interconnected systems', Annals of Systems Research, 3, 61-80 (1973).
15. Sandell, N. R., P. Varaiya, M. Athans and M. G. Safonov, 'Survey of decentralized control methods for large scale systems', IEEE Trans. Automat Control, 23, 108-128 (1978).
16. Hill, DJ. and P.J. Moylan, 'Dissipative dynamical systems: basic input-output and state properties', J. Franklin Inst., 309(5), 327-357 (1980).
17. Safonov, M. G., Stability and Robustness of Multivariable Feedback Systems, MIT Press, Cambridge, 1980.
18. Rantzer, A. and A. Megretski, 'System analysis via integral quadratic constraints', Proc. IEEE Conf. on Decision and Control, Lake Buena Vista, Florida, December 1994, pp. 3062-3067.
19. Glattfelder, A.H. and W. Schaufelberger, 'Stability analysis of single loop control systems with saturation and anti reset-windup circuits', IEEE Trans. Automat Control, 28(12), 1074-1081 (1983).
20. Doyle, J. C., R. S. Smith and D. F. Enns, 'Control of plants with input saturation nonlinearities', Proc. IEEE Conf. on Decision and Control, Minneapolis, MN, 1987, pp. 1034-1038.
21. Kothare, M. V., P. J. Campo and M. Morari, 'A unified framework for the study of anti-windup reset', Technical Report CIT-CDS 93-011, Caltech, June 1993.
22. Bernstein, D. S. and W. M. Haddad, 'Nonlinear controllers for positive-real systems with arbitrary input nonlinearities', Proc. American Control Conf, volume 1, San Francisco, California, June 1993, pp. 832-836.
23. ∞ model reduction problem', Syst. Control Letters, 20(2), 99-107 (1993).
24. Wang, W., J. Doyle and K. Glover, 'Model reduction of LFT systems', Proc. IEEE Conf. on Decision and Control, volume 2, Brighton, UK, December 1991, pp. 1233-1238.
25. Beck, C., J. C. Doyle and K. Glover, 'Model reduction of multi-dimensional and uncertain systems', Technical Report CIT/CDS 94-017, California Institut of Technology, November 1994.
26. Beck, C., J. C. Doyle and K. Glover, 'Model reduction of multi-dimensional and uncertain systems', IEEE Trans. Automat Control, 41(10), 1466-1477 (1996).
27. El Ghaoui, L. and G. Scorletti, 'Control of rational systems using linear-fractional representations and linear matrix inequalities', Automatica, 32(9), 1273-1284 (1996).
28. Scorletti, G. and L. El Ghaoui, 'Improved linear matrix inequalities conditions for gain-scheduling', Proc. IEEE Conf. on Decision and Control, New Orleans, Louisiana, December 1995, pp. 3626-3631.
29. 2-gain control of LFT systems', Proc. IEEE IMACS Multiconference on Comp. Eng. in Syst. Appl, Lilies, France, July 1996, pp. 1240-1245.
30. Willems, J. C., The Analysis of Feedback Systems, volume 62 of Research Monographs, MIT Press, Cambridge, Massachusetts, 1969.
31. Zhou, K., J. C. Doyle and K. Glover, Robust and Optimal Control, Prentice Hall, New Jersey, 1995.
32. Vidyasagar, M., Input/Output Analysis of Large-scale Interconnected Systems, Number 29 in Lecture Notes in Control and Information Sciences, Springer-Verlag, Berlin, 1981.
33. Goh, K.C. and M.G. Safonov, 'Robust analysis, sectors and quadratic functional', Proc. IEEE Conf. on Decision and Control, New Orleans, Louisiana, USA, 1995, pp. 1988-1993.
34. Vandenberghe, L. and S. Boyd, 'Semidefinite programming', SIAM Review, 38(1), 49-95 (1996).
35. Nesterov, Y. and A. Nemirovsky, Interior-point Polynomial Methods in Convex Programming, Number 13 in Studies in Applied Mathematics, SIAM, Philadelphia, 1994.
36. Boyd, S. and L. El Ghaoui, 'Method of centers for minimizing generalized eigenvalues', Linear Algebra and Applications, special issue on Numerical Linear Algebra Methods in Control, Signals and Systems, 188, 1171-1176 (1993).
37. El Ghaoui, L., F. Oustry and M. Aitrami, 'A cone complementary linearization algorithm for static output-feedback and related problems', IEEE Trans. Automat Control, 42(8), (1997).
38. Goh, K. C, L. Turan, M. G. Safonov, G. P. Papavassilopoulos and J. H. Ly, 'Biaffine matrix inequality properties and computational methods', Proc. American Control Conf., Baltimore, Maryland, June 1994, pp. 850-851.
39. Pyatnitskii, E. S., 'Absolute stability of nonstationary nonlinear systems', Automation and Remote Control, 31(1), 1-11 (1970).
40. Wood, G. D., P. J. Goddard and K. Glover, 'Approximation of linear parameter-varying systems', Proc. IEEE Conf. on Decision and Control, December 1996.
41. Doyle, J. C, 'Analysis of feedback systems with structured uncertainties', IEE Proc., 129-D(6), 242-250 (1982).
42. Sideris, A., 'Elimination of frequency search for robustness tests', IEEE Trans. Automat Control, 37(10), 1635-1640 (1992).
43. El Ghaoui, L. and H. Lebret, 'Robust solutions to least-squares problems with uncertain data matrices', SIAM J. Matrix Anal. Appl, (1996) to appear.
44. Smith, R. and A. Packard, 'Optimal control of perturbed linear static systems', IEEE Trans. Automat Control, 41(4), 579-584 (1996).
45. El Ghaoui, L., R. Nikoukhah and F. Delebecque, LMITOOL: A Front-end for LMI Optimization, Users's Guide, February 1995. Available via anonymous ftp to ftp.ensta.fr, under /pub/elghaoui/lmitool.
46. Megretsky, A. and S. Treil, 'Power distribution inequalities in optimization and robustness of uncertain systems', Journal of Mathematical Systems, Estimation, and Control, 3(3), 301-319 (1993).
47. Shamma, J. S., 'Robust stability with time-varying systems structured uncertainty', IEEE Trans. Automat Control, 39(4), 714-724, (1994).
48. El Ghaoui, L. and J. P. Folcher, 'Multiobjective robust control of LTI systems subject to unstructured perturbations', Syst. Control Letters, 28, 23-30 (1996).
49. Yakubovich, V. A., 'Minimization of quadratic functionals under the quadratic constraints and the necessity of a frequency condition in the quadratic criterion for absolute stability of nonlinear control systems', Soviet Math. Doklady, 14(2), 593-597 (1973).
50. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, volume 15 of Studies in Appl. Math. SIAM, Philadelphia, June 1994.
51. ∞ control', Int. J. Robust and Nonlinear Control, 4, 421-448 (1994)
52. ∞ control problem: LMI existence conditions and state space formulas', Automatica, 30(8), 1307-1317 (1994).