Analysis of periodically forced uncertain feedback systems

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications

Volumn 50, Issue 2, 2003, Pages 244-258

  Jönsson, Ulf T ^a   Kao, Chung Yao ^b   Megretski, Alexandre ^b  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

^b MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Harmonic analysis; Integral quadratic constraint (IQC); Periodic systems; Robustness

Indexed keywords

CONSTRAINT THEORY; ESTIMATION; FEEDBACK; HARMONIC ANALYSIS; INTEGRAL EQUATIONS; MATHEMATICAL OPERATORS; NONLINEAR CONTROL SYSTEMS; OPTIMIZATION; ROBUSTNESS (CONTROL SYSTEMS); TIME VARYING SYSTEMS; TRANSFER FUNCTIONS; UNCERTAIN SYSTEMS;

CONVEX OPTIMIZATION; INTEGRAL QUADRATIC CONSTRAINTS; UNCERTAIN FEEDBACK SYSTEM;

SYSTEM STABILITY;

EID: 0037302429     PISSN: 10577122     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCSI.2002.808218     Document Type: Article

References (33)

1. B. Alkire and L. Vandenberghe, "Convex optimization problems involving finite autocorrelation sequences," Math. Prog., Ser. A, vol. 93, no. 3, 2002, submitted for publication.
2. S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, "Linear matrix inequalities in system and control theory," in SIAM Studies in Applied Mathematics. Philadelphia, PA: SIAM, 1994.
3. S. P. Boyd and C. H. Barratt, Linear Controller Design-Limits of Performance. Englewood Cliffs, NJ: Prentice-Hall, 1991.
4. R. W. Brocket, Finite Dimensional Linear Systems. New York: Wiley, 1970.
5. L. O. Chua, C. A. Desoer, and E. S. Kuh, Linear and Nonlinear Circuits. New York: McGraw-Hill, 1987.
6. R. D'Andrea, "Convex and finite dimensional conditions for controller synthesis with dynamic integral constraints," IEEE Trans. Automat. Contr., vol. 46, pp. 222-234, Feb. 2001.
7. C. A. Desoer and M. Vidyasagar, Feedback Systems: Input-Output Properties. New York: Academic, 1975.
8. M. Farkas, Periodic Motions. New York: Springer-Verlag, 1994.
9. Y. Genin, Y. Nesterov, and P. Van Dooren, "Positive transfer functions and convex optimization," in Proc. Euro. Control Conf., 1999.
10. J.-L. Goffin and J.-P. Vial. (1999) Convex nondifferentiable optimization: A survey focused on the analytical center cutting plane method. Tech. Rep., Dept. Management Studies, University of Geneva, Switzerland. [Online]. Available:http://www.crt.unmontreal.ca/jlg/.
11. S. R. Hall and N. M. Wereley, "Generalized nyquist stability criterion for linear time periodic systems," in Proc. Amer. Control Conf., San Diego, CA, May 1990, pp. 1518-1524.
12. G. H. Hardy, T. E. Littlewood, and G. Polya, Inequalities. Cambridge, U.K: Cambridge Univ. Press, 1952.
13. D. H. Jacobson, D. H. Martin, M. Pachter, and T. Geveci, Extensions of Linear-Quadratic Control Theory. New York: Springer-Verlag, 1980.
14. U. Jönsson, C.-Y. Kao, and A. Megretski, "Robustness analysis of periodic systems," in Proc. IEEE Conf. Decision and Control 1999, Phoenix, AZ, Dec. 1999, pp. 1839-1844.
15. ____, "Robustness analysis of periodic trajectories," IEEE Trans. Automat. Contr., to be published.
16. C.-Y. Kao and A. Megretski, "Fast algorithms for solving IQC feasibility and optimization problems," in Proc. Amer. Control Conf., Arlington, VA, 2001, pp. 3019-3024.
17. C.-Y. Kao, A. Megretski, and U. Jönsson, "A cutting plane algorithm for robustness analysis of periodic systems," IEEE Trans. Automat. Contr., vol. 46, pp. 579-592, Apr. 2001.
18. C.-Y. Kao, "Efficient computational methods for robustness analysis," Ph.D. dissertation, MIT, Cambridge, MA, 2002.
19. A. Megretski and A. Rantzer, "System analysis via integral quadratic constraints," IEEE Trans. Automat. Contr., vol. 42, pp. 819-830, June 1997.
20. A. V. Megretski, "Fixed points in systems under an integral quadratic constraint," Vestnik Leningradskogo Universiteta. Matematika, vol. 23, no. 3, pp. 30-34, 1990.
21. E. Möllerstedt, "Dynamic analysis of harmonics in electrical systems," Ph.D. dissertation, Dept. Automatic Control, Lund Inst. Technol., Lund, Sweden, 2000.
22. E. Möllerstedt and B. Bernhardsson, "Out of control because of harmonics-An analysis of the harmonic response of an inverter locomotive," IEEE Control Syst. Mag., vol. 20, no. 4, pp. 70-81, 2000.
23. Yu. Nesterov and A. Nemirovski, "Interior point polynomial methods in convex programming," in Studies in Applied Mathematics. Philadelphia, PA: SIAM, 1993, vol. 13.
24. A. Rantzer and A. Megretski, "Harmonic analysis of nonlinear and uncertain systems," in Proce. Amer. Control Conf., Philadelphia, PA, 1998.
25. L. Vandenberghe and S. Boyd, "Semidefinite programming," SIAM Rev., vol. 38, pp. 49-95, 1996.
26. J. C. Willems, The Analysis of Feedback Systems. Cambridge, MA: MIT Press, 1971.
27. V. A. Yakubovich, "The method of matrix inequalities in the theory of stability of nonlinear controlled systems. I: The absolute stability of forced vibrations," Avtomatica i Telemekhanika, vol. 25, no. 7, pp. 1017-1029, 1964.
28. ____, "S-procedure in nonlinear control theory," Vestnik Leningradskogo Universiteta. Matematika, pp. 62-77, 1971.
29. ____, "A linear-quadratic optimization problem and the frequency theorem for periodic systems. I," Sibirski Matematicheskii Zhurnal, vol. 27, no. 4, pp. 181-200, 1986.
30. ____, "Frequency theorem for periodic systems and the theory of analytical design of regulators," in Method of Lyapunov Functions in Analysis of Systems Dynamics, V. M. Matrosov and L. Yu. Anapolsky, Eds. Novosibirisk, Russia: Nauka, 1987.
31. V. A. Yakubovich and V. M. Starzhinskij, Linear Differential Equations with Periodic Coefficients. Moscow, Russia: Nauka, 1972.
32. G. Zames and P. L. Falb, "Stability conditions for systems with monotone and slope-restricted nonlinearities," SIAM J. Control, vol. 6, no. 1, pp. 89-108, 1968.
33. ∞ norm computations of linear continuous-time periodic systems via the skew analysis of frequency response operators," Automatica, vol. 38, pp. 1381-1387, 2002.