Lyapunov Conditions for Uniform Asymptotic Output Stability and a Relaxation of Barbalat's Lemma

Autor:	Karafyllis, Iasson, Chaillet, Antoine
Rok vydání:	2020
Předmět:	Mathematics - Optimization and Control Electrical Engineering and Systems Science - Systems and Control
Druh dokumentu:	Working Paper
Popis:	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. Comment: 26 pages, submitted to Automatica for possible publication
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2012.07607 Zobrazit plný text záznamu View this record from Arxiv