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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...
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...
For Popov’s frequency-domain inequality a general solution is constructed in , which relies on the strict positive realness of a generating function. This solution allows revealing time-domain properties, equivalent to the fulfilment of Popov’s inequality in the frequency-domain. Particular aspects occurring in the dynamics of the linear subsystem involved in Popov’s inequality are further explored for step response, as representing a usual characterization in control system analysis. It is also...
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