A dissipation inequality for the minimum phase property

IEEE Transactions on Automatic Control

Volumn 53, Issue 3, 2008, Pages 821-826

  Ebenbauer, Christian ^a   Allgöwer, Frank ^b  

^a MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

^b UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Dissipation inequality; Minimum phase property; Nonlinear systems

Indexed keywords

CONTROL NONLINEARITIES; CONTROL THEORY;

DISSIPATION INEQUALITY; INPUT-OUTPUT NORMAL FORM; MINIMUM PHASE PROPERTY;

NONLINEAR CONTROL SYSTEMS;

EID: 42649128413     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.919517     Document Type: Article

References (24)

1. B. Aulbach, Gewöhnliche Differenzialgleichungen, 2nd ed. Heidelberg, Germany: Elsevier Spektrum Akademischer Verlag, 2004.
2. J. A. Ball, M.A. Petersen, and A. van der Schaft, "Inner-outer factorization for nonlinear invertible systems," IEEE Trans. Autom. Control, vol. 49, no. 4, pp. 483-492, Apr. 2004.
3. H. W. Bode, "Relations between attenuation and phase in feedback amplifier design," Bell Syst. Tech. J., vol. 19, pp. 421-454, 1940.
4. C. Ebenbauer and F. Allgöwer, "Mininimn-phase property of nonlinear systems in terms of a dissipation inequality," in Proc. Amer. Control Conf. (ACC), Boston, MA, 2004, pp. 1737-1742.
5. C. Ebenbauer and F. Allgöwer, "Stability analysis of constrained control systems: An alternative approach," Syst. Control Lett., vol. 56, no. 2, pp.93-98, 2007.
6. J. S. Freudenberg and D. P. Looze, "Right half plane poles and zeros and design tradeoffs in feedback systems," IEEE Trans. Autom. Control, vol. 30, no. 6. pp. 555-565, Jun. 1985.
7. E. Griepentrog, "Index reduction methods for differential-algebraic equations," in Proc. Berliner Semin. Differ. Algebr. Equ. Semin. Notes, 1992, pp. 14-29, Mathematik-92-1, ISSN: 0863-0976..
8. D. Henrion and A. Garulli, Positive Polynomials in Control. New York: Springer-Verlag, 2004.
9. A. Isidori, Nonlinear Control Systems, 3rd ed. New York: Springer-Verlag, 1994.
10. H.K. Khalil, Nonlinear Systems, 3rd ed. New York: Prentice-Hall, 2002.
11. P. V. Kokotović and M. Arcak, "Constructive nonlinear control: A historical perspective," Automatica, vol. 37, pp. 637-662, 2001.
12. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems. New York: Wiley, 1972.
13. D. Liberzon, S. Morse, and E. D. Sontag, "Output-input stability and minimum-phase nonlinear systems," IEEE Trans. Autom. Control, vol. 47, no. 3, pp. 422-436, Mar. 2002.
14. B. Malgrange, Ideals of Differentiable Functions. London, U.K.: Oxford Univ. Press, 1966.
15. J. L. Massera, "Contributions to stability theory," Ann. Math., vol. 64, pp. 182-206, 1956.
16. R. H. Middleton, "Trade-offs in linear control system design," Automatica, vol. 27, pp. 281-292, 1991.
17. P. J. Moylan, "Implications of passivity in a class of nonlinear systems," IEEE Trans. Autom. Control, vol. AC-19, no. 4. pp. 373-381, Apr. 1974.
18. D. Nešić, E. Skafidas, I. M. Y. Mareels, and R. J. Evans, "Minimum phase properties for input non-affine nonlinear systems," IEEE Trans. Autom. Control, vol. 44, no. 4, pp. 868-872, Apr. 1999.
19. G. C. Newton, L. A. Gould, and J. F. Kaiser, Analytical Design of Linear Feedback Controls. New York: Wiley, 1957.
20. P. A. Parrilo and S. Lall, "Semidefinite programming relaxations and algebraic optimization in control," Eur. J. Control, vol. 9, pp. 2-3, 2003.
21. I. G. Petrovski, Ordinary Differential Equations. Englewood Cliffs, NJ: Prentice-Hall, 1966.
22. L. Qui and E. J. Davidson, "Performance limitations of nonminimum phase systems in the servomechanism problem," Automatica, vol. 29, pp. 337-349, 1993.
23. M. M. Seron, J. H. Braslavsky, P. V. Kokotović, and D. Q. Mayne, "Feedback limitations in nonlinear systems: From Bode integrals to cheap control," IEEE Trans. Autom. Control, vol. 44, no. 4, pp. 829-833, Apr. 1999.
24. F. Svaricek, "Nulldynamik linearer und nichtlinearer Systeme: Definitionen, eigenschaften und anwendungen," Automatisierungstechnik, vol. 54, no. 7, pp. 310-322, 2006.