Frequency domain state feedback and estimation

The primary purpose of this paper is to present a frequency domain compensation scheme which is completely analogous to the time domain (state-space) employment of a Luenberger state estimator for approximating a linear state variable feedback (l.s.v.f.) design. To accomplish this objective we (i) employ a ' factorization ' of the rational transfer matrix, T(s), of a given system as the product R(s)P(s) −1 , where R(s) and R(s) are ' relatively right prime ' polynomial matrices, (ii) present a frequency domain characterization of l.s.v.f. in terms of its effect on T(s) (actually on R(s) and P(s)), and (iii) extend the notion of the classical ' eliminant matrix ' of two polynomials and its determinant, the ' resultant ', to the matrix case. An example is employed to illustrate the various steps involved and some comparisons are then made to other related investigations.