Pseudo-linear algebra: A powerful tool in unification of the study of nonlinear control systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 7, Issue PART 1, 2007, Pages 711-716

  Halás, Miroslav ^a   Kotta, Ülle ^b  

^a SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^b TALLINN UNIVERSITY OF TECHNOLOGY   (Estonia)

Author keywords

Nonlinear systems; Pseudo linear algebra; Skew polynomials; Transfer Functions

Indexed keywords

CONTINUOUS TIME SYSTEMS; LINEAR ALGEBRA; NONLINEAR CONTROL SYSTEMS; NONLINEAR SYSTEMS; POLYNOMIALS; TRANSFER FUNCTIONS;

ALGEBRAIC FORMALISMS; DIFFERENCE OPERATORS; DISCRETE-TIME NONLINEAR CONTROL; POLYNOMIAL APPROACH; SHIFT-AND; SKEW POLYNOMIAL; SKEW POLYNOMIAL RING;

DISCRETE TIME CONTROL SYSTEMS;

EID: 79960947521     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20070822-3-za-2920.00117     Document Type: Conference Paper

References (16)

1. Abramov, S.A., H.Q. Le and Z. Li (2005). Uni-variate ore polynomial rings in computer algebra. Journal of Mathematical Sciences 131(5), 5885-5903. (Pubitemid 41551260)
2. Aranda-Bricaire, E., Ü. Kotta and C. Moog (1996). Linearization of discrete-time sys-tems. SIAM Journal of Control Optimization 34, 1999-2023.
3. Bronstein, M. and M. Petkovšek (1996). An intro-duction to pseudo-linear algebra. Theoretical Computer Science 157, 3-33.
4. Cohn, R. M. (1965). Difference algebra. Wiley-Interscience. New York.
5. Conte, G., C.H. Moog and A.M. Perdon (1999). Nonlinear Control Systems: An Algebraic Set-ting. Springer-Verlag. London.
6. Grizzle, J.W. (1993). A linear algebraic framework for the analysis of discrete-time nonlinear sys-tems. SIAM Journal of Control Optimization 31, 1026-1044. (Pubitemid 23700352)
7. Haláas, M. and M. Huba (2006). Symbolic compu-tation for nonlinear systems using quotients over skew polynomial ring. In: 14th Mediter-ranean Conference on Control and Automa-tion. Ancona, Italy.
8. Haláas, M. and Ü. Kotta (2007). Extension the concept of transfer function to discrete-time non-linear control systems. In: European Control Conference. Kos, Greece. Submitted.
9. Kotta, Ü. (2000). Irreducibility conditions for nonlinear input-output difference equations. In: 39th IEEE Conf. on Decision and Control. Sydney, Australia.
10. Kotta, Ü. and M. Tõnso (2004). Irreducibility conditions for discrete-time nonlinear multi-input multi-output systems. In: 6th IFAC Symposium NOLCOS. Stuttgart, Germany.
11. Kotta, Ü., A.S.I. Zinober and P. Liu (2001). Transfer equivalence and realization of non-linear higher order input-output difference equations. Automatica 37, 1771-1778. (Pubitemid 32833046)
12. Ore, O. (1931). Linear equations in non-commutativeffelds. Annals of Mathematics 32, 463-477.
13. Ore, O. (1933). Theory of non-commutative polynomials. Annals of Mathematics 32, 480-508.
14. Zhang, C. and Y. Zheng (2004). A polynomial approach to discrete-time nonlinear system con-trollability. International Journal of Control 77, 491-497.
15. Zheng, Y. and L. Cao (1995). Transfer function description for nonlinear systems. Journal of East China Normal University (Natural Science) 2, 15-26.
16. Zheng, Y., J. Willems and C. Zhang (2001). A polynomial approach to nonlinear system controllability. IEEE Transactions on Automatic Control 46, 1782-1788. (Pubitemid 33120664)