ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV)

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Issue		ESAIM: COCV Volume 5, 2000
Page(s)		395 - 424
DOI		10.1051/cocv:2000115

DOI: 10.1051/cocv:2000115

ESAIM: COCV, August 2000, Vol. 5, 395-424

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

Hartmut Logemann
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, U.K.; (hl@maths.bath.ac.uk)

Ruth F. Curtain
Mathematics Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands; (R.F.Curtain@math.rug.nl)

Received October 18, 1999. Revised March 24, 2000.

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 $\phi$ satisfies a sector condition of the form $\langle\phi(u),\phi(u)-au \rangle\leq 0$ 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 and phrases: Absolute stability, actuator nonlinearities, circle criterion, integral control, positive real, robust tracking, well-posed infinite-dimensional systems.

AMS Subject Classification: 93C10, 93C20, 93C25, 93D05, 93D09, 93D10, 93D21

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