Pole assignment in a disk for linear systems by static output feedback

This paper proposes a systematic approach for the pole assignment in a disk for continuous or discrete-time linear systems by a static output control law. It is shown that if the open-loop system satisfies some particular structural conditions, a static output feedback gain can be easily computed, using a formula that involves only the original system matrices and the parameters defining the disk. Among the conditions the system has to satisfy, the strongest one relies on a minimum phase argument. Square and non square, proper or non proper systems are considered. The main results are derived invoking the limiting behavior of the optimal linear quadratic regulator for discrete-time systems. Some other implications are also presented.