Partial state reachability of multiple linear systems in series

We explore the issue of characterizing reachability for a subset of the component systems in the series connection of multivariable linear discrete-time systems. Using tools from algebraic systems theory, partial state reachability of a series connection is characterized in terms of Toeplitz operators and coprime factorizations of the component transfer functions. Our results extend earlier results by Callier and Nahum (1975) on reachability of the series connection of two systems, as well as a more recent characterization in Fuhrmann and Helmke (2013) of the full reachability on the series connection of r≥2 linear systems.