Transmission zero assignment in linear multivariable systems. I. Square systems

The authors consider the problem of assigning transmission zeros in a linear time-invariant multivariate system. This problem complements the pole (eigenvalue) assignment problem. It is shown that the general problem can be formulated as that of finding a full rank (dynamic) output feedback matrix which assigns the eigenvalues of the given system to the locations at which the transmission zeros are to be positioned. Using the inverse of the output feedback matrix as a feedthrough term then results in a system which has transmission zeros at the desired locations