Some Insights into Certain Kind of Asymptotically Stable Lagrange Solutions of 2-D Systems on the Grounds of Lie Algebra

摘要

This paper is concerned with the analysis of 2-d (two-dimensional) discrete system whose state space representation is composed by two matrices generating a Lie algebra that is assumed to either have a mapping onto a null matrix or be solvable. Yet, Lagrange method for solving partial difference equations is adopted to pursue the conditions under which the system is asymptotically stable. In fact, this paper examines these conditions for systems with simultaneously diagonalizable and triangularizable matrices. Finally, it is worth noting that this work yields some new perspectives to the investigation of these kinds of systems.