论文标题
Lyapunov的条件均匀渐近输出稳定性和Barbalat引理的放松
Lyapunov Conditions for Uniform Asymptotic Output Stability and a Relaxation of Barbalat's Lemma
论文作者
论文摘要
当解决并非所有状态变量要求收敛到原点的控制应用程序时，渐近输出稳定性（AOS）是一个有趣的属性。 AO通常是通过调用古典工具（例如Barbashin-Krasovskii-Lasalle的不变性原理或Barbalat的引理）来确定的。然而，这些工具都没有允许预测输出收敛是否在初始条件的有限集中均匀，这可能会导致与收敛速度和鲁棒性有关的实际问题。本文的贡献是双重的。首先，我们提供了可测试的足够条件，在该条件下，这种均匀的收敛持有。其次，我们提供了Barbalat的引理的扩展，这使均匀的连续性要求放松。这两个结果首先在有限维的环境中说明，然后扩展到无限维系统。我们提供的学术示例来说明这些结果的有用性，并表明可以调用它们以在自适应控制下为系统建立统一的AO。
Asymptotic output stability (AOS) is an interesting property when addressing control applications in which not all state variables are requested to converge to the origin. AOS is often established by invoking classical tools such as Barbashin-Krasovskii-LaSalle's invariance principle or Barbalat's lemma. Nevertheless, none of these tools allow to predict whether the output convergence is uniform on bounded sets of initial conditions, which may lead to practical issues related to convergence speed and robustness. The contribution of this paper is twofold. First, we provide a testable sufficient condition under which this uniform convergence holds. Second, we provide an extension of Barbalat's lemma, which relaxes the uniform continuity requirement. Both these results are first stated in a finite-dimensional context and then extended to infinite-dimensional systems. We provide academic examples to illustrate the usefulness of these results and show that they can be invoked to establish uniform AOS for systems under adaptive control.
