Generalized signal decoupling problem with stability for discrete-time systems

This paper deals with the decoupling problems of unknown, measurable, and previewed signals. First, well-known solutions of unknown and measurable disturbance decoupling problems are recalled. Then, new necessary and sufficient 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 decoupling problems does not change; i.e., the resolving subspace to be stabilized is the same independently of the type of signal to be decoupled, no matter whether it is completely unknown, measured, or previewed. The problem has been studied through self-bounded controlled invariants, thus 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.