Stability Boundary Sensitivity in Closed-Loop Linear Systems: Analytic Characterization of Lyapunov Conditioning Under Fixed Spectral Stability

Stability Boundary Sensitivity in Closed-Loop Linear Systems: Analytic Characterization of Lyapunov Conditioning Under Fixed Spectral Stability This record contains the primary analytic benchmark: File included in this record: Stability_Boundary_Sensitivity_in_Closed-Loop_Linear_Systems_v2.3_clean.docx This document presents a fully analytic construction of a closed-loop linear time-invariant (LTI) system in which eigenvalues remain strictly in the left half-plane while Lyapunov conditioning diverges as a parameter approaches a stability boundary. The work provides: Explicit parameterized system construction Closed-form Lyapunov solution Norm growth characterization Stability boundary analysis Falsifiability conditions Clearly bounded limitations The results demonstrate that spectral stability alone does not bound Lyapunov conditioning or sensitivity near parametric stability boundaries. No new stability theory is proposed. All derivations are classical and remain within standard Lyapunov and linear systems analysis. This analytic benchmark is accompanied by a separate computational validation record: Companion record: computational_sections_v4_1.docx(Published separately under its own DOI.) The companion document provides numerical validation, solver tolerance disclosure, nonlinear perturbation exploration, and reproducibility details corresponding directly to the analytic constructions in this primary benchmark. The two records are designed to be cited independently or together, depending on whether analytic derivation or computational validation is being referenced. 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.