An existence and regularity theorem is proved for integral equationsof convolution type which contain hysteresis nonlinearities. Onthe basis of this result, frequency-domain stability criteria arederived for feedback systems with a linear infinite-dimensionalsystem in the forward path and a hysteresis nonlinearity in thefeedback path. These stability criteria are reminiscent of theclassical circle criterion which applies to static sector-boundednonlinearities. The class of hysteresis operators underconsideration contains many standard hysteresis nonlinearitieswhich are important in control engineering such as backlash (orplay), plastic-elastic (or stop) and Prandtl operators. Whilst themain results are developed in the context of integral equations ofconvolution type, applications to well-posed state space systemsare also considered.
