A recently reported Lyapunov based criterion (Singh (2014) [7]) for the asymptotic stability of two-dimensional (2-D) linear discrete systems described by the Fornasini–Marchesini second local state-space (FMSLSS) model is reviewed. It is established in this paper that, despite utilizing a more general Lyapunov matrix, Singh's criterion will never lead to an enhanced stability region in the parameter-space as compared to that obtainable via Hinamoto–Lu's criterion. 
A note on stability analysis of 2-D linear discrete systems based on the Fornasini–Marchesini second model: Stability with asymmetric Lyapunov matrix