On causality and anticausality of cascaded discrete-time systems

This brief treats a fundamental question: when two linear time-invariant, finite-dimensional systems, causal or noncausal, are cascaded, what can be said about the causality properties of the overall system? We give conditions under which the cascaded system is causal or anticausal; these conditions are related to Sylvester equations obtained from state-space data of the systems. Both discrete- and continuous-time systems are considered.