Parametrization and reliable extraction of proper compensators. (English) Zbl 1265.93122
Summary: 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.
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