State-space realization of input-output nonlinear difference equations

ECC 1997 - European Control Conference

Volumn , Issue , 1997, Pages 3386-3391

  Kotta, U ^a   Liu, P ^b   Zinober, A S I ^b  

^a TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

^b UNIVERSITY OF SHEFFIELD   (United Kingdom)

Author keywords

Discrete time systems; Nonlinear control

Indexed keywords

DIFFERENCE EQUATIONS; DIGITAL CONTROL SYSTEMS; DISCRETE TIME CONTROL SYSTEMS;

DISCRETE - TIME SYSTEMS; DISCRETE-TIME NONLINEAR SYSTEMS; NON LINEAR CONTROL; NONLINEAR DIFFERENCE EQUATIONS; REALIZATION PROBLEMS; SINGLE INPUT SINGLE OUTPUT; STATE SPACE REALIZATION; STATE SPACE SYSTEMS;

NONLINEAR EQUATIONS;

EID: 84929094769     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.1997.7082636     Document Type: Conference Paper

References (23)

1. Aranda-Bricaire, E., and U. Kotta. Dynamic disturbance decoupling for discrete-time nonlinear systems: a linear algebraic solution. Proc. IF AC Conf. on System Structure and Control, Nantes, 155-160, 1995
2. Aranda-Bricaire, E., and U. Kotta. Dynamic disturbance decoupling for discrete-time nonlinear systems: a solution in terms of generalized controlled invariance. Proc. 35th IEEE CDC, Kobe, Japan, 4317-4318, 1996
3. Aranda-Bricaire, E., and U. Kotta. Equivalence of nonlinear systems to prime systems under generalized output transformations. Proc. ECC'97, Brussels, 1997
4. Aranda-Bricaire, E., U. Kotta, and C. H. Moog. Linearization of discrete-time systems. SIAM J. Control Optim., 34, 1999-2023, 1996
5. Cohn, R. M. Difference Algebra, Interscience Publishers, John Wiley, New York, 1965
6. Delaleau, E. and M. Fliess. Algorithme de structure, filtrations et découplage, C. R. Acad. Sci. Paris, t. 315, Série I, 101-106, 1992
7. Fliess, M. 1980, Generating series for discrete-time nonlinear systems. IEEE Trans. Automatic Control, 25, 984-985, 1980
8. Fliess, M. Should the theories for continuous time and discrete-time linear and nonlinear system really look alike? Proc. IFAC Symp. on Nonlinear Control System Design, Capri, 1989
9. Fliess, M. 1990, Automatique en temps discret et algèbre aux différences Forum Math., 2, 213-232, 1990
10. Grizzle, J. W. A linear algebraic framework for the analysis of discrete-time nonlinear systems. SIAM J. Control Optim., 31, 1026-1044, 1993
11. Hammer,. J. Non-linear systems: stability and rationality. Int. J. Control, 40, 1-35, 1984
12. B. Jakubczyk. Invertible realizations of nonlinear discrete-time systems. Proc. Conf. Inf. Sci. and Systems, 235-239, 1980
13. Kotta, U. Decoupling of discrete-time nonlinear systems by minimal order dynamic state feedback. Proc. Estonian Academy of Sciences. Phys. Math., 42, 308-319, 1993
14. Leontaritis, I. J. and S. A. Billings. Input-output parametric models for nonlinear systems. Part I: deterministic non-linear systems. Int. J. Control, 41, 303-328, 1985
15. Levin, A. U. and K. S. Narendra. Recursive identification using feedforward neural networks. Int. J. Control, 61, 533-547, 1995
16. Levin, A. U. and K. S. Narendra. Control of nonlinear dynamical systems using neural networks - Part II: Observability, identification and control. IEEE Trans, on Neural Networks, 7, 30-42, 1996
17. Mahmoud, N. A. and H. K. Khalil. Robust tracking for nonlinear systems represented by input-output models. Proc. 33rd IEEE CDC, Lake Buena Vista, 1720-1725, 1994
18. Monaco, S. and D. Normand-Cyrot. On the realization of nonlinear discrete-time system. Systems and Control Letters, 2, 145-152, 1984
19. Monaco, S. and D. Normand-Cyrot. Finite Volterra series realizations and input-output approximations of nonlinear discrete-time systems. Int. J. Contr., 47, 1771-1787, 1987
20. Nijmeijer, H. and A. J. Van Der Schaft. Nonlinear Dynamical Control Systems, Springer Verlag, New York, 1990
21. Rugh, W. J. Nonlinear System Theory, Johns Hopkins Univ Press, Baltimore-London, 1981
22. Sontag, E. D. Polynomial Response Maps, Lecture Notes in Control and Inf. Sci., N13, Springer-Verlag, Berlin, 1979
23. Zheng, Y. F., P. Liu, A. S. I. Zinober and C. H. Moog. What is the dimension of the minimal realization of a nonlinear system? Proc. 34th IEEE CDC, New Orleans, 4239-4244, 1995