Cascaded System

A Cascaded System is a composition of systems where the output of one system is the input of the next.

Categorical Structure

In Category Theory, cascading is exactly Composition of morphisms. If $H_1$ and $H_2$ are LTI systems, the cascade $H_2\circ H_1$ is their composed morphism. Composition is associative, so $(H_3\circ H_2)\circ H_1=H_3\circ (H_2\circ H_1)$.