EAP - Proceedings of the Estonian Academy of Sciences

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proceedings
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Algebraic formalism of differential p-forms and vector fields for nonlinear control systems on homogeneous time scales; pp. 215–226

PDF | doi: 10.3176/proc.2013.4.02

Authors

Zbigniew Bartosiewicz, Ülle Kotta

, Ewa Pawłuszewicz, Maris Tõnso, Małgorzata Wyrwas

Abstract

The paper develops further the algebraic formalism for nonlinear control systems defined on homogeneous time scales. The delta derivative operator is extended to differential p-forms and vector fields.

References

1. Conte, G., Moog, C. H., and Perdon, A. M. Algebraic methods for nonlinear control systems, 2nd edition. Lecture Notes Control Inform. Sci., 2007, 242.

2. Grizzle, J. W. A linear algebraic framework for the analysis of discrete-time nonlinear systems. SIAM J. Contr. Optim., 1993, 31, 1026–1044.
http://dx.doi.org/10.1137/0331046

3. Aranda-Bricaire, E., Kotta, Ü., and Moog, C. H. Linearization of discrete-time systems. SIAM J. Contr. Optim., 1996, 34, 999–2023.
http://dx.doi.org/10.1137/S0363012994267315

4. Halás, M., Kotta, Ü., Li, Z., Wang, H., and Yuan, C. Submersive rational difference systems and their accessibility. In Proceedings of the 39th 2009 International Symposium on Symbolic and Algebraic Computation (ISSAC), Seoul, Korea. 2009, 175–182.

5. Bartosiewicz, Z., Kotta, Ü., Pawłuszewicz, E., and Wyrwas, M. Algebraic formalism of differential one-forms for nonlinear control systems on time scales. Proc. Estonian Acad. Sci., 2007, 56, 264–282.

6. Kotta, Ü. and Tõnso, M. Realization of discrete-time nonlinear input-output equations: polynomial approach. Automatica, 2012, 48, 255–262.
http://dx.doi.org/10.1016/j.automatica.2011.07.010

7. Kotta, Ü., Bartosiewicz, Z., Nõmm, S., and Pawłuszewicz, E. Linear input-output equivalence and row reducedness of discrete-time nonlinear systems. IEEE Trans. Autom. Contr., 2011, 56, 1421–1426.
http://dx.doi.org/10.1109/TAC.2011.2112430

8. Belikov, J., Kotta, Ü., and Leibak, A. Transfer matrix and its Jacobson form for nonlinear control systems on time scales: CAS implementation. ATP J. Plus, 2011, 2, 6–12.

9. Casagrande, D., Kotta, Ü., Tõnso, M., and Wyrwas, M. Transfer equivalence and realization of nonlinear input-output delta-differential equations on homogeneous time scales. IEEE Trans. Autom. Contr., 2010, 55, 2601–2606.
http://dx.doi.org/10.1109/TAC.2010.2060251

10. Kotta, Ü., Bartosiewicz, Z., Pawłuszewicz, E., and Wyrwas, M. Irreducibility, reduction and transfer equivalence of nonlinear input-output equations on homogeneous time scales. Syst. & Contr. Lett., 2009, 58, 646–651.
http://dx.doi.org/10.1016/j.sysconle.2009.04.006

11. Kotta, Ü., Rehak, B., and Wyrwas, M. Reduction of MIMO nonlinear systems on homogeneous time scales. In 8th IFAC Symposium on Nonlinear Control Systems, Bologna, Italy. 2010, 1249–1254.

12. Bartosiewicz, Z., Kotta, Ü., Pawłuszewicz, E., and Wyrwas, M. Control systems on regular time scales and their differential rings. MCSS: Math. Contr. Sign. Syst., 2011, 22, 185–201.
http://dx.doi.org/10.1007/s00498-011-0058-7

13. Bohner, M. and Peterson, A. Dynamic Equations on Time Scales. Birkhäuser, Boston, 2001.
http://dx.doi.org/10.1007/978-1-4612-0201-1

14. Cohn, R. M. Difference Algebra. Wiley-Interscience, New York, 1965.

15. Bryant, R. L., Chern, S. S., Gardner, R. B., Goldschmitt, H. L., and Griffiths, P. A. Exterior Differential Systems, Vol. 18. Springer, New York, 1991.
http://dx.doi.org/10.1007/978-1-4613-9714-4

16. Belikov, J., Kaparin, V., Kotta, Ü., and Tõnso, M. NLControl website, www.nlcontrol.ioc.ee.

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