Representation of solutions of discrete linear delay systems with non permutable matrices

TL;DR

This paper introduces a new discrete delayed exponential matrix that represents solutions of discrete linear delay systems without requiring the matrices to commute, expanding the theoretical framework for such systems.

Contribution

It presents a novel discrete delayed exponential that does not rely on matrix commutativity, broadening the applicability of solution representations for delay systems.

Findings

Provides a new representation of solutions for discrete delay systems

Eliminates the need for matrix commutativity in solution formulas

Extends theoretical understanding of discrete linear delay systems

Abstract

We introduce a discrete delayed exponential depending on sequence of matrices. This discrete matrix gives a representation of a solution to the Cauchy problem for a discrete linear system with pure delay with sequence of matrices. We discard the commutativity condition used in recent works related to the representation of solutions for discrete delay linear systems.