New solution to a problem in Luenberger observer design

The matrix LA¿QL=TD, which arises in the design of a Luenberger observer to control the system dx/dt=Ax+Bu, y=Dx, is solved subject to mild restrictions. T is taken as dyadic, T=¿efT, Q cyclic, having no eigenvalues in common with A, and there results L = P¿1(Q)[e, Qe, .., Qn¿1e] SN. P(Q) and S involve the characteristic polynomial of A, and N transforms A to companion form in accordance with C=NAN¿1.