Absauret-The study of general linear multivariable systems, with p ibly different controlled and measmed outputs, is wntinned in this part of thepaper.Thesbndurematrioes,definedinPartI,areusedtosdvethe feedback realization problem. Feedback realizable transfer fnnctiwp are then used to solve problems 'of uregulator t ype. " It is shown that the solutions to problems like disturbance depoupliug, output regolation, a d pole placement are all sperial cases of the sohaion to a more general problem.Finally,itis~~howtheresoltsofPartIandPartIIcenbe c o m b i i to wke problems of "servo t ype" and of %gulator type"SimUltaneonsly.
I. INTRODUC~ONT HE control configuration in Fig. 1
was introduced inPart I of this paper. The assumptions on the linear system S and the requirements on the controller R were specified. Generalized polynomials were introduced to describe the system and the left and right structure matrices were defined. It was shown how the left structure matrix can be used to describe the class X of all transfer functions from u, toy.This led to simple solutions to problems like model matching, decoupling and invertibility.In this part of the paper we w i l l consider the class %of all transfer functions from e to y in Fig. 1. This class is somewhat difficult to describe because an F E S depends on the controller R in a nonlinear way. We w i l l circumvent this difficulty by introducing feedback realizable transfer functions. A transfer function for the controller R f in Fig. 2 is feedback realizable if it can be obtained as the transfer from e to u for some admissible controller R in Fig. 1.The point is that an F E S depends linear& on R,. Necessary and sufficient conditions for a transfer function to be feedback realizable will be derived. This result will make it possible for us to derive a linear equation which completely describes 9. Necessary and sufficient conditions for the existence of solutions to problems like dis-
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