Eigenvalue assignment by static output feedback - on a new solvability condition and the computation of low gain feedback matrices

In this article, the static output feedback problem for linear time-invariant systems is considered. For arbitrary assignability of the roots of the characteristic polynomial by static output feedback, a new necessary and sufficient condition is derived. Although, the proof is based on simple analysis, the known sufficient conditions (derived by techniques of algebraic geometry) are directly covered. Furthermore, an algorithm for the calculation of feedback matrices assigning a desired set of eigenvalues is proposed. This algorithm does not require the desired eigenvalues to be distinct and it explicitly exploits the available degrees of freedom for reducing the feedback gain. The presented approach is illustrated on computational examples.