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State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra
Kybernetika, Tome 48 (2012) no. 6, pp. 1100-1113 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows to simplify the existing step-by-step algorithm-based solution. The paper presents explicit formulas to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The method is straight-forward and better suited for implementation in different computer algebra packages such as \textit{Mathematica} or \textit{Maple}.
In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows to simplify the existing step-by-step algorithm-based solution. The paper presents explicit formulas to compute the differentials of the state coordinates directly from the polynomial description of the nonlinear system. The method is straight-forward and better suited for implementation in different computer algebra packages such as \textit{Mathematica} or \textit{Maple}.
Classification : 62A10, 93E12
Keywords: nonlinear control systems; input-output models; realization; pseudo-linear algebra 
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Belikov, Juri; Kotta, Ülle; Tõnso, Maris. State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra. Kybernetika, Tome 48 (2012) no. 6, pp. 1100-1113. http://geodesic.mathdoc.fr/item/KYB_2012_48_6_a2/

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