Reducibility condition for nonlinear discrete-time systems: behavioral approach

• Autorzy: Bartosiewicz Z. , Kotta U. , Pawłuszewicz E. , Tonso M. , Wyrwas M.
• Języki publikacji: EN

Abstrakty

EN

The paper addresses the problem of reducibility of nonlinear discrete-time systems, described by implicit higher order difference equations where no a priori distinction is made between input and output variables. The reducibility definition is based on the concept of autonomous element. We prove necessary reducibility condition, presented in terms of the left submodule, generated by the row matrix, describing the behavior of the linearized system, over the ring of left difference polynomials. Then the reducibility of the system implies the closedness of the submodule, like in the linear time-invariant case. In the special case, when the variables may be specified as inputs and outputs and the system equations are Niven in the explicit form, the results of this paper yield the known results.

Słowa kluczowe

EN

nonlinear discrete-time systems reducibility; behavioral approach; left difference polynomials

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2013
• Tom: Vol. 42, no. 2
• Strony: 329--346
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Bartosiewicz Z.

• Faculty of Computer Science Bialystok University of Technology Wiejska 45A, 15-351 Białystok, Poland

autor

Kotta U.

• Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia

autor

Pawłuszewicz E.

• Faculty of Mechanical Engineering Bialystok University of Technology Wiejska 45C, 15-351 Białystok, Poland

autor

Tonso M.

• Institute of Cybernetics at Tallinn University of Technology, Akadeemia tee 21, 12618 Tallinn, Estonia

autor

Wyrwas M.

• Faculty of Computer Science Bialystok University of Technology Wiejska 45A, 15-351 Białystok, Poland

Bibliografia

• 1. Blomberg, H. and Ylinen, R. (1983) Algebraic Theory for Multivariable Linear Systems. Academic Press, London.
• 2. Bourles, H. (2005) Structural properties of discrete and continuous linear time-varying systems: a unified approach. In: F. Lamnabhi-Lagarrique, A. Loria, and E. E. Panteley, eds., Advanced Topics in Control Systems Theory. Lecture Notes in Control and Information Science 311. Springer, London, 225–280.
• 3. Conte, G., Moog, C. and Perdon, A. (2007) Algebraic Methods for Nonlinear Control Systems. Theory and Applications., 2nd ed. Springer, London.
• 4. Fliess, M. (1990) Some basic structural properties of generalized linear systems. Systems and Control Letters 15, 391–396.
• 5. Halas, M., Kotta, Ü., Li, Z., Wang, H. and Yuan, C. (2009) Submersive rational difference systems and their accessibility. In: Proceedings of the 2009 International Symposium on Symbolic and Algebraic Computation. (New York, NY, USA, 2009), ISSAC’09. ACM. New York, 175–182.
• 6. Kotta, Ü., Bartosiewicz, Z., Nõmm, S. and Pawłuszewicz, E. (2011) Linear input-output eqiuvalence and row reducedness of discrete-time nonlinear systems. IEEE Transaction on Automatic Control 56(6), 1421–1426.
• 7. Kotta, Ü ., Pawłuszewicz, E. and Nõmm, S. (2004) Generalization of transfer equivalence for discrete-time non-linear systems: comparison of two definitions. International Journal of Control 77(3), 741–747.
• 8. Kotta, Ü. and Tõnso, M. (2012) Realization of discrete-time nonlinear input-output equations: polynomial approach. Automatica 48(2), 255–262.
• 9. Kotta, U., Zinober, A. and Liu, P. (2001) Transfer equivalence and realization of nonlinear higher order input-output difference equations. Automatica 37, 1771–1778.
• 10. Marinescu, B. and Bourlès, H. (2009) An intrinsic algebraic setting for poles and zeros of linear time-varying system. Systems and Control Letters 58, 248–253.
• 11. NLControl website (2013) www.nlcontrol.ioc.ee.
• 12. Polderman, J. W. and Willems, J. C. (1998) Introduction to Mathematical Systems Theory: a behavioral approach. Springer-Verlag, New York.
• 13. Pommaret, J.-F. (2001) Partial Differential Control Theory. Vol. II Control Systems. Mathematics and Its Applications 530. Kluwer Academic Publishers, Dordrecht.
• 14. van der Schaft, A. (2011) State maps from integration by parts. SIAM Journal on Control and Optimization 49(6), 2415–2439.
• 15. Toth, R. (2010) Modeling and Identification of Linear Parameter-Varying Systems. Lecture Notes in Control and Information Sciences 403. Springer, Germany.
• 16. Willems, J. C. (2007) The behavioral approach to open and interconnected systems. IEEE Control Systems Magazine 27, 46–99.