On a boundary value problem of a singular discrete time system with a singular pencil

TL;DR

This paper investigates boundary value problems for singular discrete-time systems with singular matrix pencils, establishing conditions for solutions and providing formulas for unique solutions, supported by numerical examples.

Contribution

It offers necessary and sufficient conditions for solution existence and uniqueness in singular discrete-time systems with singular pencils, along with solution formulas and analysis of optimal solutions.

Findings

Conditions for existence and uniqueness of solutions

Formulas for solutions in singular systems

Numerical examples validating the theory

Abstract

In this article, we study a boundary value problem of a class of singular linear discrete time systems whose coefficients are non-square constant matrices or square with a matrix pencil which has an identically zero determinant. By taking into consideration that the relevant pencil is singular, we provide necessary and sufficient conditions for existence and uniqueness of solutions. In addition, a formula is provided for the case of unique solutions and optimal solutions are studied for the cases of no solutions and infinite many solutions. Finally, based on a singular discrete time real dynamical system, numerical examples are given to justify our theory.