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 fi??xed dynamics for noninteracting control. These fi??xed dynamics are a central issue in studying noninteracting control with stability. The class of quasi??-static state feedbacks is used.
Key words:?? nonlinear systems??, controlled invariance,?? quasi-??static state feedback.