关于asymptotic stability

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关键词：Asymptotic Stability Ability asymp tabi

From Wikipedia, the free encyclopedia

Various types of stability may be discussed for the solutions of differential equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Lyapunov. In simple terms, if all solutions of the dynamical system that start out near an equilibrium point xe stay near xe forever, then xe is Lyapunov stable. More strongly, if xe is Lyapunov stable and all solutions that start out near xe converge to xe, then xe is asymptotically stable. The notion of exponential stability guarantees a minimal rate of decay, i.e., an estimate of how quickly the solutions converge. The idea of Lyapunov stability can be extended to infinite-dimensional manifolds, where it is known as structural stability, which concerns the behavior of different but "nearby" solutions to differential equations. Input-to-state stability (ISS) applies Lyapunov notions to systems with inputs.

用ε-δ语言定义asymptotic stability的时候，其中，“δ can be chose”是什么意思，怎么理解？