This question is posed in the context of the real application of control systems, not just simulations or theory.
In control theory, one can find several kinds of stability. In that regard, one can consider that finite-time stability is better than asymptotic stability, just to mention an example. However, what happens in practice? Is it a considerable difference in the closed-loop system performance when one achieves one or other stability?
For instance: In certain cases, achieving finite-time stability can throw terms in the control law that are not differentiable at the origin or even aggressive for the system. In those cases, it is sometimes preferable to implement asymptotic controllers, although the theoretic stability they achieved is not the best as those controllers that result in finite-time stability of the closed-loop system in question.
Besides, the timescale of the system can play an important role. It is highly different controlling bioreactors and quadrotors, to mention an example.
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