Computational Validation and Nonlinear Perturbation Exploration for Stability Boundary Sensitivity in Closed-Loop Linear Systems

Computational Validation and Nonlinear Perturbation Exploration for Stability Boundary Sensitivity in Closed-Loop Linear Systems This record contains the computational validation companion to the analytic benchmark on stability boundary sensitivity. File included in this record: computational_sections_v4_1.docx This document provides numerical confirmation and structured perturbation exploration corresponding to the analytic results presented in: Stability_Boundary_Sensitivity_in_Closed-Loop_Linear_Systems_v2.3_clean.docx(Published separately under its own DOI) Specifically, this computational companion includes: Explicit solver settings and tolerances Numerical Lyapunov equation verification Monte Carlo parameter sweeps Stability boundary confirmation Nonlinear perturbation exploration Growth-rate validation Reproducibility protocol All computations remain within classical linear systems and nonlinear perturbation analysis frameworks. No new stability theory is introduced. The purpose of this document is reproducibility, validation, and adversarial testing of the analytic benchmark. This record is intended to strengthen transparency and reproducibility for the analytic derivations contained in the companion DOI. The analytic benchmark and computational validation are structured as complementary but independently citable research artifacts. License: Copeland Resonant Harmonic Formalism (CRHC v1.0) This work is licensed under the Copeland Resonant Harmonic Copyright (CRHC v1.0). Attribution is required for all uses. Collaboration, academic discussion, and non-commercial use are permitted. Commercial use, resale, or incorporation into proprietary systems is not permitted without explicit written permission from the author. Derivative works must preserve attribution and must not remove or alter the stated license terms.