Authority-Limited Survivability in Delayed Nonlinear Systems

This paper establishes structural survivability limits in delayed nonlinear systems subject to bounded actuation. Rather than characterizing stability solely through spectral delay margins, we identify inequality-based constraints that govern collapse in authority-limited regimes. Three results are derived: A Riccati comparison lemma providing a model-agnostic finite-time blow-up envelope under bounded forcing. A hyperbolic delay-authority scaling bound demonstrating that minimum control authority diverges as the delay approaches its critical margin. A Lyapunov lower-bound theorem proving finite survivability time under exponential growth when actuation authority grows at most linearly in time. Application to the saturated delayed inverted pendulum confirms a two-ceiling topology: (i) a local hyperbolic delay ceiling imposed by delayed correction, and (ii) a global integral authority ceiling imposed by exponential instability. In authority-limited regimes, collapse arises predominantly from authority exhaustion rather than purely spectral transition. The framework is controller-agnostic and applies broadly to nonlinear delayed systems with bounded control.