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

¹ Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, U.K.; hl@maths.bath.ac.uk.
² Mathematics Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands; R.F.Curtain@math.rug.nl.

Received: 18 October 1999
Revised: 24 March 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 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.