In this paper

the reachability Gramian K

observability Gramian W and noise Gramian WN of2-D systems are extended to multidimensional （n-D） multi-input multi-output （MIMO） digital systems. An exPlicit relationship betWeen W and WN is derived. It is shown that: （1） for general n-D systems

the Gramians Kand WN satisfy a pair of modified discrete-time Lyapunov matrix equations （DTLME）; （2） for the causal recursive separable denominator （CRSD） n-D systems

both K and WN are block-diagonal matrices

and they can becomputed by solving n pairs of DTLME.