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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...

Szegő's first limit theorem in terms of a realization of a continuous-time time-varying systems

Pablo Iglesias, Guoqiang Zang (2001)

International Journal of Applied Mathematics and Computer Science

It is shown that the limit in an abstract version of Szegő's limit theorem can be expressed in terms of the antistable dynamics of the system. When the system dynamics are regular, it is shown that the limit equals the difference between the antistable Lyapunov exponents of the system and those of its inverse. In the general case, the elements of the dichotomy spectrum give lower and upper bounds.

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