Necessary conditions for the controllability on linear systems with positive control are presented. The real case is analyzed and the Jordan form representation is employed. The minimum number of necessary controls to obtain controllability is remarked.
In this paper we study a kind of even degree polynomials of a special form. Necessary and sufficient conditions are given in order to decide if such polynomials have all their roots on the unit circle. Next, we apply these results to obtain sufficient conditions to have the Schur stability of a segment of polynomials.