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We review the polynomial matrix compensator equation X_lD_r + Y_lN_r = Dk (COMP), e.g. (Callier and Desoer, 1982, Kučera, 1979; 1991), where (a) the right-coprime polynomial matrix pair (N_r, D_r) is given by the strictly proper rational plant right matrix-fraction P = N_rD_r, (b) Dk is a given nonsingular stable closed-loop characteristic polynomial matrix, and (c) (X_l, Y_l) is a polynomial matrix solution pair resulting possibly in a (stabilizing) rational compensator given by the left fraction...

The polynomial matrix equation $X_l{D}_r$ $+$ $Y_l{N}_r$ $=$ $D_k$ 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 $N_r{D}_r^{-1}$ 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...