Determining Observations for Stability and Bifurcation on a Finite Time Interval in Variational Control Systems with a Parameter
Author(s):
D. Yu. Kalinchenko
Abstract:
Stability and bifurcation on a finite time interval
for a thermovisco-elastoplastic contact problem are considered.
To describe such a type of contact Coulomb's law for dry friction, which is written
as a variational inequality is used. The contact problem is presented as a parameter
dependent variational system. Phase spaces for the system are given by
scales of Hilbert spaces. Determining observation operators for
bifurcation of the system and output convergence are introduced.
The frequency theorem is applied in order to describe stability and
the bifurcation which is understood as a loss of stability on
a finite time interval. Frequency-domain conditions for the existence of
determining observations and for absolute dichotomy of a variational
equation are given. The connection between the frequency-domain condition
and the completeness defect of the observation operator is considered.
Keywords
- bifurcation on a finite time
- determining observation
- frequency theorem
- interval
- variational inequality
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