A parametrization of dynamical output-feedback compensators that will assign a complete set of distinct eigenvalues to a given state-space system is presented. The main result is a compact parametric expression for the gain matrices of an output-feedback compensator, of dynamical order I > n − (m + r), explicitly characterized by two sets of free parameters: the set of n + l closed-loop system eigenvalues and a set of N = mr − n + (m + r − 1)/ effective free parameters for n-state, r-input, m-output systems. These latter N effective free parameters are determined by a sequential design procedure. The principal benefits of the explicit characterization of a parametric class of dynamical output-feedback compensators lie in the ability to directly accommodate various different design criteria.
P. Hippe, J. O'Reilly
International Journal of Control