Authority-Limited Survivability in Delayed Nonlinear Systems
Year: 2026
Type: article
Abstract: 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.
Author: Childers, Will
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7130323648
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