2025/11/25 by Itziar Baragaña, Baragaña, I., F. Puerta +3
Engineering · Computer Science · #Stability and Control of Uncertain Systems #Control Systems and Identification #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2511.20029
Given a controllable system (F,G), a local parametrization is obtained for the set of feedback gain matrices K such that the state matrix, F+GK, 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 parametrization and a local system of coordinates is provided using a diffeomorphism between this set of state feedback matrices and the orbit space of a set of truncated observability matrices via de action of a Lie group.