Making space for more zeros

The authors examine the role which is played by transfer function null spaces and incomplete images in the theory of zeros for multi-input multi-output dynamical systems. The basic notion has been to regard these spaces as generalized zeros, and to treat them together with more traditional forms of multivariable zeros, also regarded as spaces, to give broad analyses of problems such as feedback zero creation and transmission signal blocking in feedback architectures. The authors discuss a generalization of the adage on poles in the feedback compensator path becoming zeros of the resulting feedback systems. The blocking aspect of zeros, with Kalman-output-type modules, are examined to determine the effects of dynamic compensation