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<p>In this article, we introduce a family of double-index linear difference equations and develop a framework for their analysis by defining appropriate operators. These operators are used to derive explicit general solutions and to study the structural properties of the system. We further explore the characteristic equation associated with the system, providing insights into its stability, and construct the transfer matrix to describe the system’s input–output behavior in the context of control theory. A numerical example is provided to demonstrate the applicability of the method.</p>

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ON SYSTEMS OF DOUBLE-INDEX LINEAR DIFFERENCE EQUATIONS

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年8月28日

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  • Ioannis Dassios

摘要

In this article, we introduce a family of double-index linear difference equations and develop a framework for their analysis by defining appropriate operators. These operators are used to derive explicit general solutions and to study the structural properties of the system. We further explore the characteristic equation associated with the system, providing insights into its stability, and construct the transfer matrix to describe the system’s input–output behavior in the context of control theory. A numerical example is provided to demonstrate the applicability of the method.