Signal decoupling with preview: perfect solution for nonminimum-phase systems in the geometric approach context

The problem of making the output insensitive to an exogenous input signal possibly known with preview is tackled in the geometric approach context. The definition of minimal preview for decoupling is introduced. 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 minimal complexity of the solution is guaranteed by using the minimal self-bounded controlled invariant subspace. In the presence of unstable dynamics of that subspace, a steering along zeros technique completely devised in the state space allows the solution with internal stability to be nonetheless achieved. Implementation is obtained by resorting to FIR systems.