Irreducibility, reduction and transfer equivalence of nonlinear input-output equations on homogeneous time scales

Systems and Control Letters

Volumn 58, Issue 9, 2009, Pages 646-651

  Kotta, Ülle ^a   Bartosiewicz, Zbigniew ^b   Pawłuszewicz, Ewa ^b   Wyrwas, Małgorzata ^b  

^a TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

^b BIALYSTOK UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

differential field; Continuous time systems; Discrete time systems; Nonlinear control systems; Polynomials; Reduction; Time scale

Indexed keywords

DIFFERENTIAL FORMS; DIFFERENTIAL POLYNOMIAL; DISCRETE-TIME SYSTEMS; NONLINEAR INPUTS; SUFFICIENT CONDITIONS; TIME SCALE;

CONTROL; DIFFERENTIAL EQUATIONS; DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS; NONLINEAR CONTROL SYSTEMS; NONLINEAR EQUATIONS; POLYNOMIALS;

CONTINUOUS TIME SYSTEMS;

EID: 67650253883     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2009.04.006     Document Type: Article

References (20)

1. Kotta Ü., Zinober A.S.I., and Liu P. Transfer equivalence and realization of nonlinear higher order input-output difference equations. Automatica 37 (2001) 1771-1778
2. Conte G., Moog C.H., and Perdon A.M. Algebraic Methods for Nonlinear Control Systems. Theory and Applications. 2nd ed. (2007), Springer
3. Ü. Kotta, Irreducibility conditions for nonlinear input-output difference equations, in: Proc. of the 39th IEEE CDC. Sydney, Australia, 2000
4. Kotta Ü., Pawłuszewicz E., and Nømm S. Generalization of transfer equivalence for discrete-time non-linear systems: Comparison of two definitions. Int. J. Control 77 8 (2004) 741-747
5. Crouch P.E., Lamnabhi-Lagarrigue F., and van der Schaft A.J. Adjoint and Hamiltonian input-output differential equations. IEEE Trans. Automat. Control AC-40 (1995) 603-615
6. Zheng Y.F., Willems J.C., and Zhang C. A polynomial approach to nonlinear system controllability. IEEE Trans. Automat. Control 46 11 (2001) 1782-1788
7. Anderson S.R., and Kadirkamanathan V. Modelling and identification of nonlinear deterministic systems in delta-domain. Automatica 43 (2007) 1859-1868
8. Middleton R.H., and Goodwin G.C. Digital Control and Estimation: A Unified Approach (1990), Prentice Hall, NJ, Englewood Cliffs
9. Bohner M., and Peterson A. Dynamic Equations on Time Scales (2001), Birkhäuser, Boston
10. M. Halás, Ü. Kotta, Pseudo-linear algebra: A powerful tool in unification of the study of nonlinear control systems, in: NOLCOS 2007: 7th IFAC Symposium on Nonlinear Control Systems, Pretoria, South Africa, 2007
11. Monaco S., and Normand-Cyrot D. A unified representation for nonlinear discrete-time and sampled dynamics. J. Math. Syst. Estimation Control 7 4 (1995) 477-503
12. Grizzle J.W. A linear algebraic framework for the analysis of discrete-time nonlinear systems. SIAM J. Control Optim. 31 4 (1993) 1026-1044
13. Cohn R. Difference Algebra (1965), Wiley-Interscience, New York
14. Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz, M. Wyrwas, Algebraic formalism of differential one-forms for nonlinear control systems on time scales, in: Proc. Estonian Acad. Sci. Phys. Math., vol. 3, 2007
15. McConnell J.C., and Robson J.C. Noncommutative Noetherian Rings (1987), Birkhäuser
16. Bronstein M., and Petkovšek M. An introduction to pseudo-linear algebra. Theoret. Comput. Sci. 157 1 (1996) 3-33
17. D. Casagrande, Ü. Kotta, M. Wyrwas, M. Tønso, Transfer equivalence and reduction of nonlinear delta differential equations on homogeneous time scale, in: 2008 American Control Conference, Seattle, Washington, USA, 2008
18. M. Halás, Ü. Kotta, Z. Li, H. Wang, C. Yuan, Submersive rational difference systems and their accessibility, in: Proc. of the 34th International Symposium on Symbolic and Algebraic Computation, Seoul, 2009 (in press)
19. Aranda-Bricaire E., Kotta Ü., and Moog C. Linearization of discrete-time systems. SIAM J. Control Optim. 34 6 (1996) 999-2023
20. Z. Bartosiewicz, Ü. Kotta, E. Pawłuszewicz, M. Wyrwas, Irreducibility conditions for nonlinear input-output equations on homogeneous time scales, in: Preprints of 7th IFAC Symposium on Nonlinear Control Systems, 2007