Asymptotic stability refers to the property of a dynamical system where, after a disturbance, the system's state not only returns to an equilibrium point but does so in a manner that it converges to that point as time approaches infinity. This concept is crucial in control systems because it ensures that systems can recover from perturbations and maintain desired performance levels. A system that is asymptotically stable will exhibit behavior where the effects of disturbances diminish over time, making it predictable and reliable.
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