An Eigenvalue Characterization of Multivariable System Zeros

Since B (s) and d(s) are coprime, the proof is complete. From the lemma, the blocking zeros are seen to coincide with the roots, counting multiplicities, of q(s) = 0. For the sake of comparison, we remark that Rosenbrock [3] defines the zeros of G(s) to be the roots of cl(s)cz(s). . c,(s)=O. Desoer and Schulman [ I ] and Wolovich [2], without specifying multiplicities, identify the roots of c,(s)=O as the zeros of G(s). It is important to note that the blocking zeros introduced differ, in general, both in calue and in multiplicity from these other types of zeros. Thus, for the example given in (2) the Smith-McMillan form can be calculated to be