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In order to better understand the dynamics of acute leukemia, and in particular to find
theoretical conditions for the efficient delivery of drugs in acute myeloblastic leukemia,
we investigate stability of a system modeling its cell dynamics. The overall system is a cascade connection of sub-systems consisting of distributed
delays and static nonlinear feedbacks. Earlier results on local asymptotic stability are
improved by the analysis of the linearized...
The following time delay system
is considered, where may have discontinuities, in particular at the origin. The solution is defined using the “redefined nonlinearity” concept. For such systems sliding modes are discussed and a frequency domain inequality for global asymptotic stability is given.
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...
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