On the Eigenvalue Placement by Static Output Feedback Via Quantifier Elimination

The static state feedback controller design, which achieves a desired behavior of the closed loop system, was solved in linear control theory decades ago. This is not true for static output feedback controller design, which is still an open problem. Here an approach is presented which handles the existence and design problem using quantifier elimination methods. Our approach allows the formal verification of arbitrary eigenvalue placement and enables the construction of controllers which lead to specified dynamic behavior. The design method is illustrated on examples known from literature.