  In this note, we discuss the extension of several important stable square
matrices, e.g., D-stable matrices, diagonal dominance matrices,
Volterra-Lyapunov stable matrices, to their corresponding non-square matrices.
The extension is motivated by some distributed control-related problems, such
as decentralized unconditional stability and decentralized integral
controllability for non-square processes. We will provide the connections of
conditions between these special square matrices and their associated
non-square counterparts. Some conjectures for these special matrices are
proposed for future research.
