Generalized signal decoupling problem with stability for discrete-time systems

This paper deals with the decoupling problems of unknown, measurable, and p reviewed signals. First, well-known solutions of unknown and measurable dis turbance decoupling problems are recalled. Then, new necessary and sufficie nt constructive conditions for the previewed signal decoupling problem are proposed. The discrete-time case is considered. In this domain, previewing a signal by p steps means that the kth sample of the signal to be decoupled is known p steps in advance. The main result is that the stability condition for the mentioned decouplin g problems does not change; i.e., the resolving subspace to be stabilized i s the same independently of the type of signal to be de.. coupled, no matte r whether it is completely unknown, measured, or previewed. The problem has been studied through self-bounded controlled invariants, th us minimizing the dimension of the resolving subspace which corresponds to the infimum of a lattice. The reduced dimension of the resolving controlled invariant subspace reduces the order of the controller units.