Lyapunov Stability Theory ✍️
It is an easy way to see if a system will settle down at its balanced resting point. Think of the resting point as the bottom of a bowl. You set up a specific "height" measurement that is zero only at the bottom and higher everywhere else. If this height always goes down as the system moves, like a ball rolling downhill, then no matter where you start nearby, the system will slide down and stay at the bottom forever. The red spiral path in the picture shows this happening. This shows the system is stable and will return to balance after small disturbances, without needing to solve complicated math.