Talk:Exponential stability

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Systems: Control theory Mid‑importance This article is within the scope of WikiProject Systems, which collaborates on articles related to systems and systems science.SystemsWikipedia:WikiProject SystemsTemplate:WikiProject SystemsSystems Mid This article has been rated as Mid-importance on the project's importance scale. This article is within the field of Control theory.

Asymptotic stability is a general concept in dynamical systems. An equilibrium point of a dynamical system is said to be globally asymptotically stable if all trajectories of the system, regardless of the initial condition, converge to it. An equilibrium point is locally asymptotically stable if all trajectories which begin in some neighborhood of the equilibrium point converge to it. Neither linearity nor time invariance is necessarily required. It seems that this concept should be here, instead of this article, which focuses on the LTI case. I think this article ought to be moved to something like "Asymptotic stability (linear time-invariant systems)" -- Pierremenard 02:09, 11 February 2006 (UTC)Reply

I agree. The article will mislead unfamiliar readers into thinking that exponential stability is only defined for LTI systems, which is far from true. Picamas (talk) 19:24, 7 August 2023 (UTC)Reply

Please change the lead paragraph of the article. It's extremely technical. It look more like a textbook than like an enciclopedia. Perhaps we could move the current paragraph further below, and add a less-technical paragraph as an introduction, like saying something in the lines of "In control theory, a exponentially stable linear time-invariant system (LTI) is a system which has a bounded output for an impulse."

--Alej27 (talk) 06:12, 7 January 2022 (UTC)Reply