LMI-based controller synthesis: A unified formulation and solution

International Journal of Robust and Nonlinear Control

Volumn 8, Issue 8, 1998, Pages 669-686

  Masubuchi, Izumi ^a   Ohara, Atsumi ^b   Suda, Nobuhide ^c  

^a JAPAN ADVANCED INSTITUTE OF SCIENCE AND TECHNOLOGY   (Japan)

^b OSAKA UNIVERSITY   (Japan)

^c HOSEI UNIVERSITY   (Japan)

Author keywords

Comprehensive class of lmis; Multi objective controller design; Parametrization of controllers; Unified solution

Indexed keywords

MATRIX ALGEBRA; OPTIMIZATION; PROBLEM SOLVING;

LINEAR MATRIX INEQUALITIES (LMI);

CONTROL SYSTEM SYNTHESIS;

EID: 0032119587     PISSN: 10498923     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1239(19980715)8:8<669::AID-RNC337>3.0.CO;2-W     Document Type: Article

References (30)

1. Boyd, S., L. El Ghaoui, E. Feron and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, PA, 1994.
2. Boyd, S. and L. El Ghaoui, 'Method of centers for minimizing generalized eigenvalues', Linear Algebra and Its Applications, 188/189, 63-111 (1993).
3. Nesterov, Y. and A. Nemirovskii, Interior-point Polynomial Algorithms in Convex Programming: Theory and Applications, SIAM Books, Philadelphia, 1994.
4. Vandenberghe, L. and S. Boyd, 'Semidefinite programming', SIAM Review, 38(1), 49-95 (1996).
5. Toker, O., 'On the N P-hardness of solving bilinear matrix inequalities', Proc. 1995 American Control Conference, Seattle, WA, 1995, pp. 2525-2526.
6. ∞ suboptimal controllers', Int. J. Control, 59, 1031-1051 (1994).
7. ∞ control', Int. J. Robust Nonlinear Control, 4, 421-448 (1994).
8. Iwasaki, T., 'A unified matrix inequality approach to linear control design', Ph.D. Thesis, Purdue University, IN, 1993.
9. ∞ control problem: LMI existence conditions and state space formulas', Automatica, 30(8), 1307-1317 (1994).
10. Iwasaki, T., R.E. Skelton and J.C. Geromel, 'Linear quadratic suboptimal control with static output feedback', Systems Control Letters, 23, 421-430 (1994).
11. 2 control problem', Automatica, 29(2), 373-386 (1993).
12. ∞ control: a convex optimization approach', IEEE Trans. Automat. Control, AC-36(7), 824-837 (1991).
13. ∞ control', in Trends in Control, A European Perspective, A. Ishidori (Ed), volume of the special contributions to the ECC 1995, Roma, Italy, pp. 173-216.
14. Geromel, J.C., P.L.D. Peres and J. Bernussou, 'On a convex parameter space method for linear control design of uncertain systems', SIAM J. Control Optim., 29(2), 381-402 (1991).
15. 2 guaranteed cost control for uncertain discrete-time linear systems', Int. J. Control, 57(4), 853-864 (1993).
16. Ohara, A., I. Masubuchi and N. Suda, 'Quadratic stabilization and robust disturbance attenuation using parametrization of stabilizing state feedback gains - convex optimization approach', Proc. 1993 American Control Conference, 1993, San Francisco, CA, pp. 2816-2820.
17. ∞ design with pole placement constraints: an LMI approach', IEEE Trans. Automat. Control, AC-41(3), 358-367 (1996).
18. Masubuchi, I., A. Ohara and N. Suda, 'LMI-based output feedback controller design', Proc. 1195 American Control Conference, 1995, Seattle, WA, pp. 3473-3477.
19. ∞ controllers', Systems Control Letters, 18, 61-71 (1992).
20. Wu, S.-P., S. Boyd and L. Vandenberghe, 'FIR filter design via semidefinite programming and spectral factrization', Proc. 1996 IEEE Conference on Decision and Control, Kobe, Japan, 1996, pp. 271-276.
21. Ohara, A., S. Nakazumi and N. Suda, 'Relations between a parameterization of stabilizing state feedback gains and eigenvalue locations', Systems and Control Letters, 16, 261-266 (1991).
22. Yedavalli, R.K., 'Robust root clustering for linear uncertain systems using generalized Lyapunov theory', Automatica, 29(1), 237-240 (1993).
23. Petersen, I.R., 'A stabilization algorithm for a class of uncertain linear systems', Systems and Control Letters, 8, 351-357 (1987).
24. ∞ control and quadratic stabilization of systems with parametric uncertainty via output feedback', IEEE Trans. Automat. Control., AC-37(8), 1253-1256 (1992).
25. Packard, A. and J. Doyle, "The complex structured singular value', Automatica, 29(1), 71-109 (1993).
26. Boyd, S.P. and C.H. Barratt, Linear Controller Design - Limits of Performance, Prentice-Hall, NJ, 1991.
27. Youla, D.C., J.J. Bongiorno and H.A. Jabr, 'Modern Wiener-Hopf design of optimal controllers - part I: the single-input-output case', IEEE Trans. Automat. Control, AC-21, 3-13 (1976).
28. Youla, D.C., J.J. Bongiorno and H.A. Jabr, 'Modern Wiener-Hopf design of optimal controllers - part II: the multivariable case', IEEE Trans. Automat. Control AC-21, 319-338 (1976).
29. ∞ performance bound: a Riccati equation approach', IEEE Trans. Automat. Control, AC-34(3), 293-305 (1989).
30. ∞ performance objectives', Proc. 1989 American Control Conference, Pittsburgh, PA 1989, pp. 2065-2070.