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ON THE LYAPUNOV APPROACH TO ROBUST STABILIZATION OF UNCERTAIN NONLINEAR SYSTEMS
Author(s) -
NAJSON FEDERICO,
KREINDLER ELIEZER
Publication year - 1996
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(199601)6:1<41::aid-rnc130>3.0.co;2-1
Subject(s) - lyapunov function , control theory (sociology) , lyapunov redesign , mathematics , bounded function , nonlinear system , robust control , lyapunov equation , exponential stability , lyapunov exponent , computer science , control (management) , mathematical analysis , physics , quantum mechanics , artificial intelligence
In the Lyapunov approach employed in this paper, known in the literature as Lyapunov control , or min‐max control , robust, global uniform asymptotic stability is achieved by a discontinuous control law which ensures that the Lyapunov derivative is negative despite bounded uncertainty. For that, it is assumed that the uncertainties satisfy certain matching conditions, and that a Lyapunov function for the nominal plant is available. To obtain lower control magnitudes, this paper develops control laws which counter the uncertainties on a component‐wise basis, rather than the usual normic one. Both the basic discontinuous control law, which is proved to provide robust global uniform asymptotic stability, and a continuous app roximation, which is proved to ensure global uniform ultimate boundedness, are derived. Application to model following is given. We adapt recent results on robust quadratic stabilization of nominally linear time‐invariant plants subjected to nonlinear, bo unded and unmatched uncertain perturbations, to extend our results to this important class of systems; this is illustrated by two examples.