Asymptotic Stability

Asymptotic stability refers to a system’s ability to return to a steady state after a disturbance, and to do so gradually, eventually settling exactly at that equilibrium point over time. If a system is asymptotically stable, small deviations from equilibrium diminish as time progresses, meaning the system not only stays close to its desired state but also gradually moves back to it. This concept is important in fields like engineering and control systems, ensuring that systems such as vehicles, aircraft, or robots operate reliably and smoothly without drifting away from their intended functioning.