This paper analyzes the stability of a class of discrete linear multidimensional (MD) systems, whose solutions are path dependent and may not be uniquely specified by initial conditions. Based on the concept of solvable Lie algebra and a new comparison principle, it presents a simple necessary and sufficient condition for exponential stability of the MD systems in terms of the spectral radius of the system matrices. This extends a previous result based on the pairwise commutativity of the system matrices. A numerical example is given to illustrate the present result.