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Systems with hysteresis in the feedback loop : existence, regularity and asymptotic behaviour of solutions

Hartmut Logemann, Eugene P. Ryan (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Systems with hysteresis in the feedback loop: existence, regularity and asymptotic behaviour of solutions

Hartmut Logemann, Eugene P. Ryan (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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...

Time-domain and parametric L 2 -properties corresponding to Popov inequality

Mihail Voicu, Octavian Pastravanu (2002)

Kybernetika

For Popov’s frequency-domain inequality a general solution is constructed in L 2 , 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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