Pole assignment of strictly proper and proper linear systems by constant output feedback

Abstract

A new unifying approach for the study of pole assignment by constant output feedback (CPAP) for strictly proper and proper linear systems is presented. The multilinear nature of CPAP is reduced to a linear problem and to the standard multilinear problem of decomposability of multivectors; the solvability of CPAP thus becomes a problem of finding real intersections of a linear variety with the Grassmann variety of a projective space. An alternative proof to the ml≥n(m, I, n are the numbers of outputs, inputs, states) necessary and sufficient condition for generic pole-assignability of strictly proper systems by complex output feedback is given; the above result is extended to the ml≥ n + 1 condition for the case of proper systems. Stronger necessary conditions for generic pole assignment by a real output feedback are obtained by using the recently introduced invariant, the Plucker matrix Pn such conditions are that Pn must have full rank and ml≥n (strictly proper case), or ml≥ n + 1 (proper case). It is sh...