Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra

Ülle Kotta; Palle Kotta; Miroslav Halás

Kybernetika (2010)

  • Volume: 46, Issue: 5, page 831-849
  • ISSN: 0023-5954

Abstract

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The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuous- and discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized system’ equation. The procedure is given to find the reduced (irreducible) system equation that is transfer equivalent to the original system equation. Besides unification, the tools of pseudo-linear algebra allow to extend the results also for systems defined in terms of difference, q -shift and q -difference operators.

How to cite

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Kotta, Ülle, Kotta, Palle, and Halás, Miroslav. "Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra." Kybernetika 46.5 (2010): 831-849. <http://eudml.org/doc/196324>.

@article{Kotta2010,
abstract = {The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuous- and discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized system’ equation. The procedure is given to find the reduced (irreducible) system equation that is transfer equivalent to the original system equation. Besides unification, the tools of pseudo-linear algebra allow to extend the results also for systems defined in terms of difference, $q$-shift and $q$-difference operators.},
author = {Kotta, Ülle, Kotta, Palle, Halás, Miroslav},
journal = {Kybernetika},
keywords = {nonlinear control systems; input-output models; reduction; pseudo-linear algebra; transfer equivalence; nonlinear control systems; input-output models; reduction; pseudo-linear algebra; transfer equivalence},
language = {eng},
number = {5},
pages = {831-849},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra},
url = {http://eudml.org/doc/196324},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Kotta, Ülle
AU - Kotta, Palle
AU - Halás, Miroslav
TI - Reduction and transfer equivalence of nonlinear control systems: Unification and extension via pseudo-linear algebra
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 5
SP - 831
EP - 849
AB - The paper applies the pseudo-linear algebra to unify the results on reducibility, reduction and transfer equivalence for continuous- and discrete-time nonlinear control systems. The necessary and sufficient condition for reducibility of nonlinear input-output equation is presented in terms of the greatest common left factor of two polynomials describing the behaviour of the ‘tangent linearized system’ equation. The procedure is given to find the reduced (irreducible) system equation that is transfer equivalent to the original system equation. Besides unification, the tools of pseudo-linear algebra allow to extend the results also for systems defined in terms of difference, $q$-shift and $q$-difference operators.
LA - eng
KW - nonlinear control systems; input-output models; reduction; pseudo-linear algebra; transfer equivalence; nonlinear control systems; input-output models; reduction; pseudo-linear algebra; transfer equivalence
UR - http://eudml.org/doc/196324
ER -

References

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