Shock–Recovery-Based Interpretation of Dynamic Stability in High-Dimensional Control Systems

This preprint proposes a shock–recovery-based interpretation of dynamic stabilityin high-dimensional control systems. Instead of relying on static performance metrics such as steady-state error orcapacity degradation, the framework focuses on the recovery dynamics followingexternal perturbations. The key quantity is the recovery time (τ), which reflectsthe system’s resilience and latent fragility. Using battery aging simulations based on the NASA PCoE lithium-ion dataset, we showthat instability in τ emerges significantly earlier than observable capacity loss.This behavior suggests that recovery-time instability functions as an early warningsignal for impending failure. The proposed interpretation is model-agnostic and applicable to a wide range ofcomplex systems, including batteries, energy storage systems, and high-dimensionalengineered infrastructures. The framework provides a foundation for risk-awaremonitoring and early intervention in safety-critical systems. Correspondence regarding this work can be addressed to: junlee7111@gmail.com Update (Jan 2026): The core methodologies and structural frameworks presented in this work are now protected under one or more U.S. Provisional Patent Applications (filed Jan 2026). Following the establishment of legal priority, the research is transitioning from theoretical analysis toward industrial applicability, system integration, and proof-of-concept (PoC) validation in safety-critical domains.