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Absolute stability results for well-posed infinite-dimensionalsystems with applications to low-gain integral control

Published online by Cambridge University Press:  15 August 2002

Hartmut Logemann  and
Ruth F. Curtain
Hartmut Logemann
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, U.K.; hl@maths.bath.ac.uk.
Ruth F. Curtain
Affiliation:
Mathematics Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands; R.F.Curtain@math.rug.nl.
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Abstract

We derive absolute stability results for well-posed infinite-dimensional systems which, in a sense, extend the well-known circle criterion to the case that the underlying linear system is the series interconnection of an exponentially stable well-posed infinite-dimensional system and an integrator and the nonlinearity ϕ satisfies a sector condition of the form (ϕ(u),ϕ(u) - au) ≤ 0 for some constant a>0. These results are used to prove convergence and stability properties of low-gain integral feedback control applied to exponentially stable, linear, well-posed systems subject to actuator nonlinearities. The class of actuator nonlinearities under consideration contains standard nonlinearities which are important in control engineering such as saturation and deadzone.

Keywords

Absolute stabilityactuator nonlinearitiescircle criterionintegral controlpositive realrobust trackingwell-posed infinite-dimensional systems.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 5 , 2000 , pp. 395 - 424
Copyright
© EDP Sciences, SMAI, 2000

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