Lyapunov's Stability Theorem is a fundamental principle in control theory that provides criteria for determining the stability of an equilibrium point in a dynamical system. It states that if a Lyapunov function can be found that decreases over time, the equilibrium point is stable, meaning that nearby trajectories will converge to it. This theorem connects to phase portraits by visually representing the behavior of trajectories in relation to equilibrium points, allowing for a deeper understanding of system dynamics.
congrats on reading the definition of Lyapunov's Stability Theorem. now let's actually learn it.