On the asymptotic stability analysis of a certain type of discrete-time 3-D linear systems

This work is concerned with the analysis of 3-d (3-dimensional) systems. The aim is to establish conditions that guarantee the asymptotic stability of these kinds of systems. To accomplish it, the Lagrange candidate solutions method for partial difference equations is adopted here. We show that the systems are asymptotically stable if the entries of the matrices of their state space descriptions yield a solution in the Lagrange solution sense. Furthermore, the particular cases in which the matrices can be turned into a diagonal matrix by means of the canonical transformation is studied in order to figure out the role of the eigenvalues on the stability conditions.