Relaxations of parameterized LMIs with control applications

International Journal of Robust and Nonlinear Control

Volumn 9, Issue 2, 1999, Pages 59-84

  Tuan, H D ^a   Apkarian, P ^b  

^a NAGOYA UNIVERSITY   (Japan)

^b ONERA   (France)

Author keywords

Convex relaxations; Linear parameter varying systems; LMI; Robustness analysis

Indexed keywords

LINEAR CONTROL SYSTEMS; MATRIX ALGEBRA; ROBUSTNESS (CONTROL SYSTEMS);

LINEAR PARAMETER-VARYING SYSTEMS; PARAMETERIZED LINEAR MATRIX INEQUALITIES (PLMI);

CONTROL THEORY;

EID: 0033077650     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(199902)9:2<59::AID-RNC392>3.0.CO;2-O     Document Type: Article

References (25)

1. Boyd, S., L. ElGhaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1994.
2. ∞ control', Int. J. Robust Nonlinear Control, 4, 421-448 (1994).
3. ∞ control problems: LMI existence and state space formulas', Automatica, 30, 1307-1318 (1994).
4. Nesterov, Yu. E. and A. S. Memirovski, Interior Point Polynomial Methods in Convex Programming: Theory and Applications, Vol. 13, SIAM Studies in Applied Mathematics, SIAM, Philadelphia, 1994.
5. Vanderberghe, L. and S. Boyd, 'Primal-dual potential reduction method for problems involving matrix inequalities', Math. Programm. Ser. B, 69, 205-236 (1995).
6. Ben-Tal, A. and A. Memirovski, 'Robust convex programming', Working paper.
7. Apkarian, P. and H. D. Tuan, 'Parameterized LMIs in control theory', SIAM J. Control. Optima, in press.
8. Amato, F., L. Garofalo, A. Glielmo and Pironty, 'Robust and quadratic stability via polytope set covering', Int. J. Robust. Nonlinear Control, 5, 745-756 (1995).
9. ∞ control with parametric Lyapunov functions', Systems Control Lett., 30, 57-69 (1997).
10. Watanabe, R., K. Uchica and M. Fujita, 'A new LMI approach to analysis of linear systems with scheduling parameter-reduction to a finite number of LMI conditions', Proc. CDC, 1996, pp. 1663-1665.
11. Ben-Tal, A. and A. Nemirovski, 'Robust solutions to uncertain linear problems', Technical Report 6/95, Optimization Laboratory, Technion, 1995.
12. Oustry, F., L. Elghaoui and H. Lebert, 'Robust solutions to uncertain semidefinite programs', SIAM J. Optim., in press.
13. Gahinet, P., P. Apkarian and M. Chilali, 'Parameter-dependent Lyapunov functions for real parameteric uncertainty', IEEE Trans. Automat. Control, 41, 436-442 (1996).
14. Konno, H., P. T. Thach and H. Tuy, Optimization on Low Rank Nonconvex Structures, Kluwer Academic Publishers, Boston, Dordrecht, 1997.
15. Tuy, H., Convex Analysis and Global Optimization, Kluwer Academic Publishers, Boston, Dordrecht, 1998.
16. Chen, G. and T. Sugie, 'An upper bound on μ based on the parameter dependent multiplier', Proc. ACC, 1997, pp. 2604-2608.
17. 2-norm control for LPV system with bounded parameter variations rates', Proc. ACC, 1995, pp. 2379-2383.
18. Gahinet, P., A. Nemirovski and M. Chilali,. LMI Control Toolbox, The Math. Works Inc., 1994.
19. Siljak, D. D., 'Parameter space methods for robust control design: a guided tour', IEEE Trans. Automat. Control, 34, 674-688 (1989).
20. Reichert, R. T. 'Robust autopilot design using μ synthesis', Proc. ACC, 1990, pp. 2368-2373.
21. Packard, A., 'Gain scheduling via linear fractional transformations', Systems Control Lett., 22, 79-92 (1994).
22. ∞ controllers', IEEE Trans. Automat. Control, 40, 853-864 (1995). See also p. 1681.
23. Helmersson, A., 'Methods for robust gain-scheduling', Ph.D. Thesis, Linkoping University, Sweden, 1995.
24. Scorletti, G. and L. E. Ghaoui, 'Improved linear matrix inequality conditions for gain scheduling', Proc. CDC, 1995, pp. 3626-3631.
25. Poljak, S. and J. Rohn, 'Checking robust nonsingularity is NPO-complete', Math. Control Signals Systems, 6, 1-9 (1994).