Generalized controlled invariance for nonlinear systems

A general setting is developed which describes controlled invariance for nonlinear control systems and which incorporates the previous approaches dealing with controlled invariant (co-)distributions. A special class of controlled invariant subspaces, called controllability cospaces, is introduced. These geometric notions are shown to be useful for deriving a (geometric) solution to the dynamic disturbance decoupling problem and for characterizing the so-called fixed dynamics for the general input-output noninteracting cont.rol problem via dynamic compensation. These fixed dynamics are a major issue for studying noninteracting control with stability. The class of quasi-static state feedbacks is used.