On stability of generalised systems of difference equation with non-consistent initial conditions

TL;DR

This paper investigates the stability of generalized linear difference systems with potentially singular leading coefficients under non-consistent initial conditions, providing practical stability criteria.

Contribution

It introduces new stability conditions for systems with singular matrices and non-consistent initial conditions, expanding analysis tools for such complex systems.

Findings

Derived easily testable stability conditions.

Analyzed systems with singular leading coefficients.

Focused on optimal solutions under non-consistent initial data.

Abstract

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix. We focus on the optimal solutions of the system and derive easily testable conditions for stability.