Pole assignment by gain output feedback

This short paper deals with the problem of pole assignment with incomplete state observation. It is shown that if the system is controllable and observable, and if
n \leq r + m - 1
, an almost arbitrary set of distinct closed-loop poles is assignable by gain output feedback, where
n, r
, and
m
are the numbers of state variables, inputs and outputs, respectively. This result improves considerably the ones obtained so far about this problem. Different from the conventional approach using the characteristic equation, an approach based on the properties of the eigenspaces of the closed-loop dynamics is used in this short paper, which gives a new light on the various problems in the linear system theory. It is also shown, as a direct consequence of this result, that the minimum order of the dynamic compensator required for almost arbitrary pole assignment of overall closed-loop system is not greater than
n - m - r + 1
.