  We revisit the problem of computing (robust) controlled invariant sets for
discrete-time linear systems. Departing from previous approaches, we consider
implicit, rather than explicit, representations for controlled invariant sets.
Moreover, by considering such representations in the space of states and finite
input sequences we obtain closed-form expressions for controlled invariant
sets. An immediate advantage is the ability to handle high-dimensional systems
since the closed-form expression is computed in a single step rather than
iteratively. To validate the proposed method, we present thorough case studies
illustrating that in safety-critical scenarios the implicit representation
suffices in place of the explicit invariant set. The proposed method is
complete in the absence of disturbances, and we provide a weak completeness
result when disturbances are present.
