On the observability Gramian and noise Gramian of 2-D digital systems

In this brief, it is considered the relationship between the observability Gramian W and noise Gramian W/sub N/ for 2-D digital systems (A, B, C, D). An explicit connection between W and W/sub N/ is derived as W=A/sup T/W/sub N/A+C/sup T/C. Therefore, the 2-D local observability could be detected by W rather than W/sub N/ in general.