On the existence and approximation of a dissipating feedback
Abstract
Given a matrix $A\in \R^{n\times n}$ and a tall rectangular matrix $B \in \R^{n\times q}$, $q < n$, we consider the problem of making the pair $(A,B)$ dissipative, that is the determination of a {\it feedback} matrix $K \in \R^{q\times n}$ such that the field of values of $AB K$ 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 $K$.
 Publication:

arXiv eprints
 Pub Date:
 October 2018
 arXiv:
 arXiv:1811.00069
 Bibcode:
 2018arXiv181100069G
 Keywords:

 Mathematics  Optimization and Control