360
Views
29
CrossRef citations to date
0
Altmetric
Flat Systems of Finite Dimension

Conditions for the existence of a flat input

&
Pages 439-443 | Accepted 09 Jul 2007, Published online: 06 Oct 2010

References

  • Bestle , D and Zeitz , M . 1983 . Canonical form observer design for non-linear time variable systems . Int. J. Control , 38 : 419 – 431 .
  • Delaleau , E and Rudolph , J . 1998 . Control of flat systems by quasi-static feedback of generalized states . Int. J. Control , 71 : 745 – 765 .
  • Fliess , M , Lévine , J , Martin , P and Rouchon , P . 1992 . On differentially flat non-linear systems . C.R. de l'Académie des Sciences , 315 : 619 – 624 .
  • Fliess , M , Lévine , J , Martin , P and Rouchon , P . 1995 . Flatness and defect of non-linear systems. Introductory theory and examples . Int. J. Control , 61 : 1327 – 1361 .
  • Fliess , M , Lévine , J , Martin , P and Rouchon , P . 1999 . A Lie-Bäcklund approach to equivalence and flatness of non-linear systems . IEEE Trans. Autom. Control , 44 : 922 – 937 .
  • Graichen , K , Hagenmeyer , V and Zeitz , M . 2005 . A new approach for inversion-based feedforward control design for non-linear systems . Automatica , 41 : 2033 – 2041 .
  • Hagenmeyer , V and Delaleau , E . 2003 . Exact feedforward linearization based on differential flatness . Int. J. Control , 76 : 537 – 556 .
  • Hermann , R and Krener , A . 1977 . Nonlinear controllability and observability . IEEE Trans. Autom. Control , 22 : 728 – 740 .
  • Isidori , A . 1995 . Nonlinear Control Systems , 3rd , Springer .
  • Jakubczyk , B and Respondek , W . 1980 . On linearization of control systems . Bull. Acad. Polonaise Sci. Ser. Sci. Math. , 28 : 517 – 522 .
  • Kailath , T . 1980 . Linear Systems , Englewood Gliffs, NJ : Prentice Hall .
  • Krabs , W . 2003 . A general predator prey model . Mathematical and Computer Modelling of Dynamical Systems , 9 : 387 – 401 .
  • Krener , A and Isidori , A . 1983 . Linearization by output injection and non-linear observers . Syst. Contr. Lett. , 3 : 47 – 52 .
  • Krener , A and Respondek , W . 1985 . Nonlinear observers with linearizable error dynamics . SIAM J. Control and Optim. , 23 : 197 – 216 .
  • Martin , P , Murray , RM and Rouchon , P . 1997 . “Flat systems” . In Plenary lectures and mini-courses, 4th European Control Conference Edited by: Bastin , G and Geverts , M . 211 – 264 . Brussels/Belgium
  • Martin , P , Murray , RM and Rouchon , P . 2001 . “Flat systems, equivalence and feedback” . In Advances in the control of non-linear systems , Edited by: Baños , A , Lamnabhi-Lagarrigue , F and Montoya , FJ . 3 – 32 . Springer-Verlag : Lecture Notes in Control and Inform. Sci. .
  • Oldenburg , J and Marquardt , W . 2002 . Flatness and higher order differential model representations in dynamic optimization . Comp. and Chem. Eng. , 26 : 385 – 400 .
  • Rothfuß , R . 1997 . Anwendung der flachheitsbasierten Analyse und Regelung nichtlinearer Mehrgrößensysteme, Fortschr.-Ber. , Vol. 8/664 , Düsseldorf, Germany : VDI Verlag .
  • Rudolph , J . 2005 . Flachheit: Eine nützliche Eigenschaft auch für Systeme mit Totzeiten . at - Automatisierungstechnik , 53 : 178 – 188 .
  • Sira-Ramirez , H and Agrawal , SK . 2004 . Differentially Flat Systems , New York : Marcel Decker, Inc. .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.