Lyapunov’s Shortcut: Stability in Motion from Brooms to Routers

We unpack Lyapunov theory—the idea that you can prove stability with a single energy-like function without solving every trajectory. From the broomstick analogy to drift-plus-penalty in queuing networks, we show how a simple V knob lets you trade stability for energy cost, and how this framework underpins modern control, robotics, and even personal balance.

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