On the number of special feedback configurations in linear modular systems

This paper deals with a state feedback in linear modular systems (LMSs) defined over a finite field F q . By means of a state feedback, any controllable LMS S can be converted to a closed loop system having a desired characteristic polynomial p ( s ) . Given a polynomial p ( s ) , we calculate the number of state feedback matrices which result in single input controllable closed loop systems having a characteristic polynomial p ( s ) .