Homogeneous linear matrix difference equations of higher order: Singular case
Charalambos P. Kontzalis, Grigoris Kalogeropoulos
TL;DR
This paper investigates the solutions of higher-order homogeneous linear matrix difference equations in the singular case, establishing conditions for existence and uniqueness when the matrix pencil is singular.
Contribution
It provides necessary and sufficient conditions for the existence and uniqueness of solutions in the singular case of higher-order matrix difference equations.
Findings
Conditions for solution existence in singular cases
Criteria for solution uniqueness
Analysis of matrix pencil singularity impact
Abstract
In this article, we study the singular case of an homogeneous generalized discrete time system with given initial conditions. We consider the matrix pencil singular and provide necessary and sufficient conditions for existence and uniqueness of solutions of the initial value problem.
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Taxonomy
TopicsDifferential Equations and Numerical Methods · Matrix Theory and Algorithms · Numerical methods for differential equations