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In a previous paper  we have introduced the notion of "almost controlled invariant subspaces" which are subspaces to which one can steer the state of a linear system arbitrarily close. In the present paper we will show how these subspaces my be viewed as ordinary controlled invariant subspaces when one allows distributional inputs, or as those subspaces which can be approximated by controlled invariant subspaces. The results are applied to a number of control synthesis problems, i.e., disturbance decoupling, robustness, noisy gain stabilization, and cheap control. Part II of the paper will treat the dual theory of almost conditionally invariant subspaces.
Date of Publication: Feb 1981