A necessary and sufficient minimality condition for uncertain systems

IEEE Transactions on Automatic Control

Volumn 44, Issue 10, 1999, Pages 1802-1813

  Beck, Carolyn L ^a,b   Doyle, John ^a,c  

^a IEEE   (United States)

^b University of Illinois at Urbana Champaign   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Minimality; Model reduction; Uncertain systems

Indexed keywords

ALGORITHMS; EQUIVALENCE CLASSES; LYAPUNOV METHODS; MATHEMATICAL MODELS; MATHEMATICAL TRANSFORMATIONS; MATRIX ALGEBRA; STATE SPACE METHODS;

LINEAR FRACTIONAL TRANSFORMATIONS; LINEAR MATRIX INEQUALITIES; MINIMALITY; MODEL REDUCTION;

UNCERTAIN SYSTEMS;

EID: 0033331760     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/9.793720     Document Type: Article

References (32)

1. J. C. Doyle, "Analysis of feedback systems with structured uncertainties," Proc. Inst. Elec. Eng., pt. D, pp. 242-250, 1982.
2. M. Safonov, "Stability margins of diagonally perturbed multivariable feedback systems," Proc. Inst. Elec. Eng., pt. D, pp. 251-256, 1982.
3. _, Stability and Robustness of Multivariable Feedback Systems. Cambridge, MA: MIT Press, 1980.
4. K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
5. G. Dullerud, Control of Uncertain Sampled-Data Systems. New York: Birkhauser, 1995.
6. P. Apkarian and P. Gahinet, "A convex characterization of gain-scheduled H-infinity controllers," IEEE Trans. Automat. Contr., vol. 40, 1995.
7. A. Packard, "Gain scheduling via linear fraction transformations," Syst. Contr. Lett., pp. 79-92, 1994.
8. J. Shamma, "Robust stability with time-varying structured uncertainty," IEEE Trans. Automat. Contr., vol. 39, Apr. 1994.
9. P. M. Young, "Robustness with parametric and dynamic uncertainty," Ph.D. dissertation, California Inst. Technol., 1993.
10. A. Packard and J. C. Doyle, "The complex structured singular value," Automatica, vol. 29, no. 1, pp. 71-109, 1993.
11. A. Megretski and S. Treil, "S-procedure and power distribution inequalities: A new method in optimization and robustness of uncertain systems," Mittag-Leffler Inst., 1991.
12. F. Paganini, "Sets and constraints in the analysis of uncertain systems," Ph.D. dissertation, California Inst. Technol., Dec. 1995.
13. C. L. Beck, "Model reduction and minimality for uncertain systems," Ph.D. dissertation, California Inst. Technol., Jan. 1996.
14. C. L Beck, J. C. Doyle, and K. Glover, "Model reduction of multidimensional and uncertain systems," IEEE Trans. Automat. Contr., vol. 41, Oct. 1996.
15. W.-M. Lu, K. Zhou, and J. C. Doyle, "Stabilization of uncertain linear systems and linear multi-dimensional systems," IEEE Trans. Automat. Contr., vol. 41, Jan. 1996.
16. C. L. Beck and J. C. Doyle, "Realizations of uncertain systems and formal power series," in Proc. American Control Conf., 1995.
17. C. L. Beck, "Minimality for uncertain systems and IQC's," in Proc. IEEE Control and Decision Conf., 1994, pp. 3068-3074.
18. C. Beck and R. D'Andrea, "Minimality, controllability and observability for uncertain systems," in Proc. American Control Conf., 1997, pp. 3130-3135.
19. P. Bendotti and C. L. Beck, "On the role of LFT model reduction methods in robust controller synthesis for a pressurized water reactor," IEEE Trans. Contr. Syst. Technol., vol. 7, Mar. 1999.
20. C. Beck and R. D'Andrea, "Computational study and comparisons of LFT reducibility methods," in Proc. American Control Conf., 1998.
21. J. Berstel and C. Reutenauer, Rational Series and Their Languages (Monographs on Theoretical Computer Science). Springer-Verlag, 1988.
22. F. Paganini and J. C. Doyle, "Analysis of implicitly defined systems," in Proc. IEEE Control and Decision Conf., 1994, pp. 3673-3678.
23. A. Megretski, "Necessary and sufficient conditions of stability: A multiloop generalization of the circle criterion," IEEE Trans. Automat. Contr., 1993.
24. R. Braatz, P. Young, J. C. Doyle, and M. Morari, "Computational complexity of μ calculation," IEEE Trans. Automat. Contr., pp. 1000-1002, 1994.
25. O. Toker, "Complexity issues in system theory and solution procedures for certain robust control problems," Ph.D. dissertation, Ohio State Univ., 1995.
26. P. Gahinet, A. Nemirovskii, A. J. Laub, and M. Chilali, The LMI Control Toolbox. Natick, MA: MathWorks, 1995.
27. F. Alizadeh, J. P. Haeberly, M. Nayakkankuppam, and M. Overton, SDPpack: New Code for Semidefinite Programming, 1997, available via http://www.cs.nyu.edu/phd_students/madhu/sdppack/sdppack.html.
28. S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory. Philadelphia, PA: SIAM, 1994.
29. R. D'Andrea and S. Khatri, "Kalman decomposition of linear fractional transformation representations and minimality," in Proc. American Control Conf., 1997, pp. 3557-3561.
30. N. K. Bose, Applied Multidimensional Systems Theory. New York: Van Nostrand Reinhold, 1982.
31. C. L. Beck and P. Bendotti, "Model reduction methods for unstable uncertain system," in Proc. IEEE Control and Decision Conf., 1997, pp. 3298-3303.
32. G. Scorletti and L. E. Ghaoui, "Improved linear matrix inequality conditions for gain-scheduling," in Proc. IEEE Control and Decision Conf., 1995.