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Robust output feedback stabilization via a small gain theorem
Author(s) -
Battilotti S.
Publication year - 1998
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/(sici)1099-1239(199803)8:3<211::aid-rnc256>3.0.co;2-9
Subject(s) - control theory (sociology) , constructive , lyapunov function , small gain theorem , nonlinear system , robust control , mathematics , class (philosophy) , output feedback , nonlinear control , implicit function theorem , computer science , stability (learning theory) , control (management) , process (computing) , physics , quantum mechanics , artificial intelligence , machine learning , operating system , mathematical analysis
In this paper, we give sufficient conditions for designing robust globally stabilizing controllers for a class of uncertain systems, consisting of ‘nominal’ nonlinear minimum phase systems perturbed by uncertainties which may affect the equilibrium point of the nominal system (‘biased’ systems). The constructive proof combines a systematic step‐by‐step procedure, based on H ∞ arguments, with a small gain theorem, recently proved for nonliner systems. At each step, one finds two Lyapunov functions, one for a state‐feedback problem and the other one for an output injection problem. Combining these two functions, one derives at each step a Lyapunov function candidate for solving an ouptut feedback stabilization problem. This approach allows one to put into a unified framework many existing results on robust output feedback stabilization. © 1998 John Wiley & Sons, Ltd.