Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions
Department of Mathematical Sciences,
University of Bath,
Bath BA2 7AY, U.K.; email@example.com. firstname.lastname@example.org.
Revised: 12 November 2002
An existence and regularity theorem is proved for integral equations of convolution type which contain hysteresis nonlinearities. On the basis of this result, frequency-domain stability criteria are derived for feedback systems with a linear infinite-dimensional system in the forward path and a hysteresis nonlinearity in the feedback path. These stability criteria are reminiscent of the classical circle criterion which applies to static sector-bounded nonlinearities. The class of hysteresis operators under consideration contains many standard hysteresis nonlinearities which are important in control engineering such as backlash (or play), plastic-elastic (or stop) and Prandtl operators. Whilst the main results are developed in the context of integral equations of convolution type, applications to well-posed state space systems are also considered.
Mathematics Subject Classification: 45M05 / 45M10 / 47J40 / 93C10 / 93C25 / 93D05 / 93D10 / 93D25
Key words: Absolute stability / asymptotic behaviour / frequency-domain stability criteria / hysteresis infinite-dimensional systems / integral equations / regularity of solutions.
© EDP Sciences, SMAI, 2003