# Full and Partial Eigenvalue Placement for Minimum Norm Static Output Feedback Control

## DOI:

https://doi.org/10.52846/stccj.2022.2.1.32## Keywords:

Linear time-invariant, eigenvalue placement, static output feedback, polynomial ideals, Gröbner bases, quantifier elimination, norm minimization## Abstract

The controller design for linear time-invariant state space systems seems to be straightforward and well established. This is not true for static output feedback control, which is still a challenging task. This paper deals with controller design based on eigenvalue assignment. We consider the placement of distinct as well as multiple real eigenvalues or complex conjugate pairs. The desired eigenvalue configurations are characterised in terms of algebraic divisibility of the characteristic polynomial of the closed-loop system. We also consider the problem of partial eigenvalue placement, where not all eigenvalues are fixed by feedback. Degrees of freedom in the controller design are used for the minimization of various matrix norms of the feedback gain matrix.

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*Syst. Theor. Control Comput. J.*, vol. 2, no. 1, pp. 22–33, Jun. 2022, doi: 10.52846/stccj.2022.2.1.32.