A sufficient condition for structural decouplability of linear nonsquare systems

This note presents a sufficient condition for structural decouplability of linear time-invariant nonsquare systems. Using graph representation for structured systems, the case of a square system (with
m
-inputs and
m
-outputs) is examined first. The condition for decouplability of this case is characterized by the existence of a "complete shortest matching" in the graph of that system. The above result plays an essential role in deriving a sufficient condition for the case of nonsquare systems. This is accomplished by reducing a nonsquare system into an appropriate square system, and trying to find a complete shortest matching after removing some arcs from the graph of the transformed system.