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 Barbălat’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 Barbălat’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.

在处理并非所有状态变量都要求收敛到原点的控制应用程序时，渐近输出稳定性 (AOS) 是一个有趣的特性。AOS 通常通过调用 Barbashin-Krasovskii-LaSalle 不变性等经典工具来建立原则或 Barbălat 引理。然而，这些工具都不允许预测输出收敛是否在有界初始条件集上一致，这可能会导致与收敛速度和鲁棒性相关的实际问题。本文的贡献是双重的。首先，我们提供了一个可测试的充分条件，在该条件下这种一致收敛成立。其次，我们提供了 Barbălat 引理的扩展，它放宽了统一连续性要求。这两个结果首先在有限维上下文中陈述，然后扩展到无限维系统。我们提供了学术示例来说明这些结果的有用性，并表明可以调用它们为自适应控制下的系统建立统一的 AOS。