A solvable Lie algebra condition for stability of linear multidimensional systems

This note analyzes exponential stability of a class of linear discrete multidimensional systems. Using a multidimensional comparison principle for estimating the system componentwise exponential convergence and a solvable Lie algebra condition, a sufficient condition for exponential stability of linear multidimensional systems is presented. The stability condition can be easily examined by computing the system matrices in finite steps. This is demonstrated by an example.