Admissible region for pole positioning with optimal regulators

A method of pole positioning using linear quadratic regulators is examined, and the admissible region of optimal closed-loop poles is determined. The design method employs successive shifting of either a single real pole or a pair of complex conjugate poles at a time. The result clarifies admissible region for both real and complex poles, and also leads to a specific design procedure. The characteristic polynomial of a Hamilton matrix associated with the regulator problem plays a key role in deriving the result