Asymptotic Stability Analysis of 2-D Discrete State Space Systems with Singular Matrix

摘要

The aim of this paper is to establish, on the basis of Lagrange method for solving partial difference equations, conditions under an asymptotic stability analysis procedure to investigate conditions for the existence of a solution to 2-D (two dimensional) discrete system whose state space representation is composed by a non-singular matrix. To accomplish it, the concept of generalized inverse of matrices and Jordan canonical transformation are applied on the original system and then Lagrange solutions to the transformed systems are pursued. Once the conditions are determined on the grounds of the transformed system and the existence conditions of solutions for this system is accomplished, the conditions for the original system is obtained by back transformation. A numerical example is given to show how the procedure works.