期刊
SYSTEMS & CONTROL LETTERS
卷 60, 期 12, 页码 1045-1050出版社
ELSEVIER
DOI: 10.1016/j.sysconle.2011.07.012
关键词
Robust stabilization; Asymptotic stability; Differential inclusions; Topology; Basin of attraction; Converse Lyapunov theory
资金
- AFOSR [FA9550-09-1-0203]
- NSF [ECCS-0925637, CNS-0720842]
- Directorate For Engineering [0925637] Funding Source: National Science Foundation
- Div Of Electrical, Commun & Cyber Sys [0925637] Funding Source: National Science Foundation
We show that when a compact set is globally asymptotically stable under the action of a differential inclusion satisfying certain regularity properties, there exists a smooth differential equation rendering the same compact set globally asymptotically stable. The regularity properties assumed in this work stern from the consideration of Krasovskii/Filippov solutions to discontinuous differential equations and the robustness of asymptotic stability under perturbation. In particular, the results in this work show that when a compact set cannot be globally asymptotically stabilized by continuous feedback due to topological obstructions, it cannot be robustly globally asymptotically stabilized by discontinuous feedback either. The results follow from converse Lyapunov theory and parallel what is known for the local stabilization problem. (C) 2011 Elsevier B.V. All rights reserved.
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