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ON THE LYAPUNOV APPROACH TO ROBUST STABILIZATION OF UNCERTAIN NONLINEAR SYSTEMS

✍ Scribed by FEDERICO NAJSON; ELIEZER KREINDLER

Publisher
John Wiley and Sons
Year
1996
Tongue
English
Weight
923 KB
Volume
6
Category
Article
ISSN
1049-8923

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✦ Synopsis

In the Lyapunov approach employed in this paper, known in the literature as Lyapunov control, or minmar 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 approximation, 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, bounded and unmatched uncertain perturbations, to extend our results to this important class of systems; this is illustrated by two examples.

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