Kybernetika 46 no. 5, 831-849, 2010

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

Ülle Kotta, Palle Kotta and Miroslav Halás

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.

Keywords:

nonlinear control systems, input-output models, reduction, pseudo-linear algebra, transfer equivalence

Classification:

93C10, 93B20, 93B25

paper.pdf

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