Formal Classical Control Framework on Bounded Phase Space Corridors

High-performance tracking controllers operating near non-linear operational boundaries frequently suffer performance degradation due to physical actuator limits. This manuscript establishes a rigorous geometric framework to map, bound, and optimize tracking performance under hard actuator saturation (uₘₐₓ). By defining continuous error metrics across phase space, we identify momentum-assisted operational corridors where closed-loop stability is preserved without exceeding physical actuator capacity. Using Lyapunov analysis restricted to the unsaturated regime, we prove regional exponential stability within a certified linear operational corridor (Ωₗᵢₙ). Furthermore, explicit normalization reference constants are provided to ensure full reproducibility across independent simulation sweeps. Peer Review & Consensus Board (Team J.A.G.): Developed and vetted in collaboration with Team J.A.G. (Alexander, Gemini, Claude, Kimi) within the Conceptual Dynamics Vault & Research Sandbox.