On the existence and approximation of a dissipating feedback

Given a matrix $A\in {\mathbb{R}}^{n\times n}$ and a tall rectangular matrix $B \in \R^{n\times q}$,$q < n$,weconsidertheproblemofmakingthepair$(A,B)$dissipative,thatisthedeterminationofafeedbackmatrix$K \in \R^{q\times n}$suchthatthefieldofvaluesof$A-B K$ lies in the left half open complex plane. We review and expand classical results available in the literature on the existence and parameterization of the class of dissipating matrices, and we explore new matrix properties associated with the problem. In addition, we discuss various computational strategies for approximating the minimal Frobenius norm dissipating $K$.