Proper feedback compensators for a strictly proper plant by polynomial equations
International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 4, p. 493.

Voir la notice de l'article dans European Digital Mathematics Library

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 C = (X_l)^{−1}Y_l . We recall first the class of all polynomial matrix pairs (X_l, Y_l) solving (COMP) and then single out those pairs which result in a proper rational compensator. An important role is hereby played by the assumptions that (a) the plant denominator D_r is column-reduced, and (b) the closed-loop characteristic matrix Dk is row-column-reduced, e.g., monically diagonally degree-dominant. This allows us to get all solution pairs (X_l, Y_l) giving a proper compensator with a row-reduced denominator X_l having (sufficiently large) row degrees prescribed a priori. Two examples enhance the tutorial value of the paper, revealing also a novel computational method.
Classification : 93B25, 93B52, 93D15
Mots-clés : polynomial matrix systems, linear time-invariant feedback control systems, flexible belt device, row-column-reduced polynomial matrices, feedback compensator design 
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     title = {Proper feedback compensators for a strictly proper plant by polynomial equations},
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Frank Callier; Ferdinand Kraffer. Proper feedback compensators for a strictly proper plant by polynomial equations. International Journal of Applied Mathematics and Computer Science, Tome 15 (2005) no. 4, p. 493. https://geodesic-test.mathdoc.fr/item/IJAMCS_2005__15_4_207761/