Exact decoupling with preview in the geometric context

The problem of making the output insensitive to an exogenous input signal known with preview is tackled in the geometric approach context. Necessary and sufficient constructive conditions for decoupling with minimal preview are proved by means of simple geometric arguments. The structural and the stabilizability conditions are considered separately. The use of self-bounded controlled invariant subspaces enables the minimal order solution to be straightforwardly derived. A steering along zeros technique is devised to solve decoupling in the presence of unstable unassignable dynamics of the minimal self-bounded controlled invariant subspace satisfying the structural constraint. The procedure is illustrated by an example often considered in the literature