Lyapunov stability is a concept from the field of dynamical systems and control theory that helps analyze the stability of equilibrium points in a system. There are several key notions associated with Lyapunov stability: 1. **Equilibrium Point**: An equilibrium point (or fixed point) of a dynamical system is a point in the state space where the system remains at rest if it starts at that point.
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An equilibrium is Lyapunov stable if every neighbourhood contains a smaller neighbourhood whose forward trajectories remain in the original neighbourhood for all time.