Stability results for decomposable multidimensional digital systems based on the Lyapunov equation

Lower bounds for the stability margins of 2-D digital systems are extended to n-D systems. These bounds are then improved for n-D (including 2-D) systems which have characteristic polynomials with 1-D factor polynomials. Stability analysts of n-D systems due to finite wordlength is considered, some tight lower bounds on coefficient wordlength which guarantee the n-D system to be stable and/or globally asymptotically stable are presented. Improved and/or extended criteria for absence of overflow oscillations and global asymptotic stability of n-D systems are proposed as well. An example is presented to illustrate the theoretical results, and it is shown that the lower bound on coefficient wordlength could be considerably improved for the (partial) factorable denominator n-D digital systems. All the discussions are based on the n-D Lyapunov equation.