A revisit to the stability of spatially interconnected systems

A necessary and sufficient condition is derived in this paper for the stability of a linear time invariant (LTI) multidimensional (MD) dynamic system. This condition is expressed by a set of linear matrix inequalities (LMIs). A special characteristic of this condition is that although the number of LMIs increases exponentially with the spatial dimension of the system, the dimensions of the LMIs are identical to each other and are of the same order as those of system matrices. Moreover, both the number and the dimensions of the LMIs are explicitly given. These properties make the derived condition particularly attractive when the spatial dimensions are low that are frequently encountered in practical applications.