Control Lyapunov Function

A Control Lyapunov Function is a mathematical tool used in control systems to ensure stability. Think of it like a landscape with a lowest point representing the desired state. The Lyapunov function assigns a value to each state, indicating how "far" it is from this goal. The control strategy adjusts inputs to always move in a direction that decreases this value, guiding the system smoothly toward the target without overshooting or instability. Essentially, it’s a method to mathematically guarantee that a system will behave predictably and settle at the desired state over time.