Uniform boundedness of solutions to linear difference equations with periodic forcing functions

Abstract

<abstract><p>In this paper we give criteria on the uniform boundedness of the solutions to linear difference equations (LEs) with periodic forcing functions. First, we give a necessary and sufficient condition that the sequence $ \{L^n\} $ of a square matrix $ L $ is bounded, from which a criterion on the uniform boundedness of the solutions to LEs is obtained. Second, a criterion on the uniform boundedness of the solutions for LEs with periodic forcing functions is given by applying a certain representation of solutions. In connection with LEs with delay, we give the characteristic equation of a matrix under the commuting condition.</p></abstract>