Absolute stability results for well-posed infinite-dimensional systems with applications to low-gain integral control
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY,
2 Mathematics Institute, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands; R.F.Curtain@math.rug.nl.
Revised: 24 March 2000
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.
Mathematics Subject Classification: 93C10 / 93C20 / 93C25 / 93D05 / 93D09 / 93D10 / 93D21
Key words: Absolute stability / actuator nonlinearities / circle criterion / integral control / positive real / robust tracking / well-posed infinite-dimensional systems.
© EDP Sciences, SMAI, 2000