Eigenvalue assignment in linear multivariable systems by output feedback

The assignment of arbitrary cloacd-loop eigenvalue spectra by output feedback is investigated in the special ease of systems for which the set of state-feedback matrices P which yield a desired closed-loop eigenvalue spectrum is finite and can be readily generated. In particular, a simple necessary and sufficient condition for the existence of an output-feedback matrix K corresponding to a prescribed state-feedback matrix P is established which also leads directly to the matrix K in cases when the condition is satisfied. The condition derived in this paper requires neither the computation of generalized inverse matrices (Munro and Vardulakis 1973), nor the transformation of state vectors (Patel 1974), nor the determination of Luenberger canonical forms (Vardulakis 1976), and indicates very clearly that an output-feedback matrix K corresponding to a prescribed state-feedback matrix P exists only in very special circumstances.