A Local Parameterization of the State‐Feedback Matrices in the Pole Assignment Problem

Given a controllable system , a local parameterization is obtained for the set of the feedback gain matrices such that the state matrix, , of the closed‐loop system is in a prescribed similarity class. It is shown that this set can be endowed with the structure of a differentiable manifold whose dimension is also computed. Then a local parameterization and a local system of coordinates are obtained using a diffeomorphism between this set of state‐feedback matrices and the orbit space of a set of truncated observability matrices via the action of a Lie group.