WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 20, 2025
Boundary Value Problems for Linear and Nonlinear Discrete Systems:
Solvability Conditions and Input-to-State Stability
Authors: ,
Abstract: This paper investigates boundary value problems (BVPs) for both linear and nonlinear discrete systems
with a focus on input-to-state stability (ISS). We begin by analyzing homogeneous and nonhomogeneous linear
systems, deriving explicit solution formulas using mathematical induction. Solvability conditions for these
systems are established, providing necessary and sufficient criteria for the existence of solutions. The study is
then extended to nonlinear discrete systems, where perturbation terms are introduced, and equivalent transformed
BVPs are derived. By applying solvability conditions, we analyze the transition from nonlinear to linear cases
as perturbations approach zero. The results contribute to the understanding of ISS properties in discrete-time
dynamical systems and serve as a foundation for stability analysis and numerical methods in solving BVPs in
discrete settings.
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Keywords: Boundary value problems, discrete systems, solvability conditions, input-to-state stability (ISS),
nonlinear dynamics, difference equations, perturbation analysis, Moore-Penrose pseudoinverse operators
Pages: 268-276
DOI: 10.37394/23203.2025.20.30