Eigensystem Clustering via Feedback Control

The eigensystem clustering in specified regions of the complex plane, is investigated for multivariable linear feedback systems. A quantitative description of feasible regions is discussed and related to a generalization of open left-half-plane stabilization problem. The design procedure is considerably simplified by adopting recursive representation of characteristic polynominals with simple real and complex eigenvalues in order to solve higher order systems. It is demonstrated that a parametrized class of feedback gains can be evaluated by means of the Cayley-Hamilton resolvant expansion. Illustration of the method, in the case of a bounded frequency region, is included.