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Original Articles
Equivalence of Discrete Time-Variant Control Systems on Time Scales
Ewa Pawłuszewiczepaw@pb.edu.plFaculty of Computer Science Department of Mathematics, Białystok TechnicalcUniversityFaculty Of Computer Science, Białystok Technical UniversityWiejska 45A, Bialystok, 15–351, PolandView full profile →
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- Published Online:
- 03 Jun 2013
- Article type:
- Original Articles
- Language:
- EN
- Article no.:
- 1726037X.2008.10698540
- Pages:
- 1–12
Abstract
The concept of dynamic equivalence of nonlinear time-variant systems defined on discrete-time scales is introduced. There are studied relations between classical static state feedback and external dynamic feedback. There is proved that if two time-variant systems defined on any discrete time scale are locally equivalent with respect to the regular static state feedback transformations then they are locally equivalent with respect to the external dynamic feedback transformations.
Keywords
References
Bartosiewicz, Z., Jakubczyk, B. and Pawłuszewicz, E.1994 . “ Dynamic feedback equivalence of nonlinear discrete-time systems ” . In Proceedings of First International Symposium on Mathematical Models in Automation and Robotics, Szczecin: Poland, Tech. Univ. of Szczecin Press . Bartosiewicz, Z. and Pawłuszewicz, E.2006 . Realizations of linear control systems on time scales . Control & Cybernetics, 35 ( 4 ) : 769 – 786 . Bartosiewicz, Z. and Pawłuszewicz, E.2008 . Realizations of nonlinear control systems on time scales . IEEE Transactions on Automatic Control, 53 ( 2 ) : 571 – 575 . Bartosiewicz, Z. and Pawłuszewicz, E.Dynamic feedback equivalence of time-variant nonlinear control systems on time scales . to appear in International Journal of Mathematics and Statistics, Bartosiewicz, Z. and Pawłuszewicz, E.Dynamic feedback equivalence of nonlinear systems on time scales . Proceedings of 16th IFAC Congress . (CD-ROM) Bohner, M. and Peterson, A.2001 . Dynamic Equation on Time Scales . Birkhäuser, Charlet, B., Levine, J. and Marino, R.1991 . Sufficient conditions for dynamic state feedback linearization . SIAM J. Control and Optimization, 29 : 38 – 57 . Fausett, L.V. and Murty, K.N.2004 . Controllability, observability and realizability criteria on time scale dynamical systems . Nonlinear Stud., 11 : 627 – 638 . Gürses, M., Guseinov, G.Sh. and Silindir, B.2005 . Integrable equations on time scales . Journal of Mathematical Physics, 46 : 113 – 501 . Hilger, S.1988 . “ Ein Maßkettenkalkülmit Anwendung auf Zentrumsmannigfaltigkeiten ” . In Ph.D. thesis, Universität WürzburgJakubczyk, B.Remarks on equivalence and linearization of nonlinear systems . Proceedings of the 2nd IFAC NOLCOS Symposium . France pp. 393 – 397 . Jakubczyk, B.1992 . Dynamic feedback equivalence of nonlinear control systemspreprint Kotta, Ü., Zinober, A.S.I. and Liu, P.2001 . Transfer equivalence and realization of nonlinear higher order input-output difference equations . Automatica, 37 : 1771 – 1778 . Pawłuszewicz, E. and Bartosiewicz, Z.1999 . “ External Dynamic Feedback Equivalence of Observable Discrete-time Control Systems ” . In Proc. of Symposia in Pure Mathematics, Vol. 64 , 73 – 89 . Providence: AMS . Pawłuszewicz, E.Static state and external dynamic transformations of discrete-time systems . Proceedings of the Sixth International Symposium on Methods and Models in Automation and Robotics MMAR’2000 . Poland Vol. 1 , pp. 283 – 287 . Pomet, J.-B.1995 . “ A differential geometric setting for dynamic equivalence and dynamic linearization ” . In Geometry in Nonlinear Control and Differential Inclusions, Vol. 32 , 319 – 339 . Banach Center Publications .
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