Feedback tames a system — until you push it too hard. Turn the loop gain up and the corrections start overshooting, then over-correcting the overshoot, and the whole thing rings, then howls: the microphone-near-speaker screech, the wobbling drone, the shower that’s never the right temperature. Stability has a limit, and crossing it flips a steadying loop into a runaway one. Slide the gain past the edge.
A feedback loop with delay is stable only up to a critical gain. Model a delayed loop xₘ₁ = xₙ − g·xₙ₋₁: for small gain g the state decays (stable), but as g rises past a threshold the correction, arriving too late, overshoots and the oscillation GROWS — the closed-loop poles cross into the right half-plane (the Nyquist/phase-margin limit). This is why every real controller has a stability margin: audio feedback howl, a drone’s wobble, a badly-tuned thermostat hunting, or a shower where your late reactions to temperature make it swing hot-cold. A fail-loud self-check throws unless low gain stays bounded while high gain grows without bound. ◆ real control theory, node-verified.
A discrete delayed-feedback toy (the exact stable-below / unstable-above-a-gain-threshold behaviour); the real boundary depends on the full loop delay and dynamics (Nyquist criterion) — the too-much-gain-oscillates result is exact.