Stability analysis of 2-d discrete systems on the basis of Lagrange solutions and doubly similarity transformed systems

This paper aims to investigate methods for analyzing the asymptotic stability of 2-dimensional (2-D) linear discrete systems with state delayed components. To achieve it, we focus on the similarity transformation of the system, which is already a similarity transformation of the original system. Then, we make use of the Lagrange method for solving the set of partial difference equations constituting the doubly transformed system to establish the conditions for the asymptotic stability of the original system.