The theory of invariant subspaces was first developed for linear systems by W. M. Wonham [Linear multivariable control: A geometric approach (1979; Zbl 0424.93001)]. In the present paper a conceptual framework for invariant structures of general dynamical systems (in the sense of M. D. Mesarovic and Y. Takahara [General systems theory: Mathematical foundations (1975; Zbl 0328.93002)] in a set theoretic approach is presented. A concept of feedback invariance is introduced and (among other results) the existence of a unique maximal feedback invariant partition is proved. A specific application to the problem of disturbance localization is discussed and two theorems are proved.