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A theorem for UGAS and ULES of (passive) nonautonomous systems: robust control of mechanical systems and ships
Author(s) -
Fossen Thor. I.,
Loría Antonio,
Teel Andrew
Publication year - 2001
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.551
Subject(s) - backstepping , exponential stability , lipschitz continuity , control theory (sociology) , robustness (evolution) , nonlinear system , mathematics , mechanical system , tracking error , stability (learning theory) , convergence (economics) , adaptive control , computer science , control (management) , mathematical analysis , economics , physics , artificial intelligence , biochemistry , chemistry , quantum mechanics , machine learning , gene , economic growth
The main contribution of this paper is a theorem to guarantee uniform global asymptotic stability (UGAS) and uniform local exponential stability (ULES) for a class of nonlinear non‐autonomous systems which includes passive systems. These properties (and a uniform local Lipschitz condition) guarantee robustness of stability while weaker properties, like uniform global stability plus global convergence, do not. Our main result is then used in the tracking control problem of mechanical systems and ships. We use an adaptive backstepping design and prove UGAS of the closed‐loop tracking error system, in particular, we obtain that both the tracking and parameter estimation errors converge uniformly globally to zero. Copyright © 2001 John Wiley & Sons, Ltd.