Boundary-Induced No-Go Limits for Global Stabilization in Large-Scale Systems Delay–Bandwidth Obstructions from Boundary Mediation

Preprint: This paper derives a necessary obstruction to global stabilization in large-scale systems whose sensing, computation, and actuation are mediated through a bandwidth-limited, delay-imposing control interface. The result identifies a coupled delay–growth limitation arising from the interaction between observation spillover and causal filtering. Main Result: For separation-principle controllers that treat spillover as unstructured contamination, stabilization requires the delay–growth product to satisfy a bound that is strictly tighter than the union of classical delay and bandwidth constraints whenever spillover exceeds a critical ratio. The obstruction arises because causal rejection of spillover necessarily incurs phase loss, tightening the delay margin. Key Contributions: A quantitative connection between classical spillover mechanisms and delay-margin degradation via Bode sensitivity limits An explicit phase-cost characterization for low-pass spillover rejection Identification of a strict interaction regime where delay and bandwidth conditions are individually satisfied yet stabilization is impossible Comparison with information-theoretic limits, showing cases where channel capacity is sufficient but stabilization still fails Scope: The results provide necessary conditions within a restricted architecture class (spillover-unaware separation-principle controllers). They do not apply to model-based estimators that explicitly exploit spillover dynamics. No claims of controller synthesis or optimality are made.