Arbitrary Pole Assignability by Static Output Feedback under Structural Contraints

Using a few elementary concepts from algebraic geometry such as multidimensional projective space, quadric hypersurface and its tangential variety, the known problem of arbitrary pole placement is transformed into a system of well‐structured (partly non‐linear) algebraic equations. Necessary and sufficient solvability conditions are derived. Finally, it is outlined how to calculate admissible output feedback matrices which ensure the desired pole assignment.