In this paper we shall solve a very general control problem in the context of the geometric approach to linear multivariable control theory.
The problem to be considered will be general in the sense that it contains as a special case not only the well-known disturbance decoupling problem by measurement feedback (cf. Schumacher ) and the problem of stabilizing the output with respect to the disturbances by means of a state feedback (cf. Hautus ), but for instance also the extension of the latter problem to the situation in which only the use of measurement feedback is allowed. Furthermore, in this paper connections with and extensions of recent work of Trentelman  will be given.
In the paper a fruitful use will be made of a merge of concepts arising from the geometric approach to control theory on the one hand and the frequency domain approach to control theory on the other hand.