Asymptotic Stability of Partial Difference Equations Systems with Singular Matrix

摘要

This paper is concerned with the asymptotic stability of partial difference equations representing 2-d (two dimensional) discrete systems that appear in practical fields as electrical engineering, automation and control, and computer and communication, among others. The partial difference equations are expressed in the state space description format and its composing matrix is singular. The aim is to establish the conditions under which the system is asymptotically stable. In order to accomplish it, the system is first augmented by means of the orthonormal matrix, then the Lagrange method for solving partial difference equations is considered to examine the stability of the overall system. Finally, a numerical example is presented to show how to apply the procedure suggested here.