An explicit pole-assigning feedback formula with application to dead-beat feedback construction in discrete linear systems

A short proof is given of the well-known theorem that in a controllable, autonomous, linear system the poles of the closed-loop system can be reassigned by means of a linear, constant state-variable feedback; the construction in the proof provides an efficient algorithm for pole assignment. In particular, we give explicitly the feedback which guarantees dead-beat performance in a reachable linear autonomous discrete-time system in steps.