Geodesic
Parametrization and reliable extraction of proper compensators
Kybernetika, Tome 38 (2002) no. 5, pp. 521-540 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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The polynomial matrix equation $X_lD_r$ $+$ $Y_lN_r$ $=$ $D_k$ is solved for those $X_l$ and $Y_l$ that give proper transfer functions $X_l^{-1}Y_l$ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function $N_rD_r^{-1}$ such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by $D_k$. The subclass is navigated and extracted through a conventional parametrization whose denominators are affine to row echelon form and the centre is in a compensator whose numerator has minimum column degrees. Applications include stabilization of linear multivariable systems.
The polynomial matrix equation $X_lD_r$ $+$ $Y_lN_r$ $=$ $D_k$ is solved for those $X_l$ and $Y_l$ that give proper transfer functions $X_l^{-1}Y_l$ characterizing a subclass of compensators, contained in the class whose arbitrary element can be cascaded to a plant with the given strictly proper transfer function $N_rD_r^{-1}$ such that wrapping the negative unity feedback round the cascade gives a system whose poles are specified by $D_k$. The subclass is navigated and extracted through a conventional parametrization whose denominators are affine to row echelon form and the centre is in a compensator whose numerator has minimum column degrees. Applications include stabilization of linear multivariable systems.
Classification : 93B52, 93C05, 93D15, 93D21
Keywords: compensator; stabilization 
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Kraffer, Ferdinand; Zagalak, Petr. Parametrization and reliable extraction of proper compensators. Kybernetika, Tome 38 (2002) no. 5, pp. 521-540. http://geodesic.mathdoc.fr/item/KYB_2002_38_5_a2/

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