ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Observation Stability and Convergence for Neural-type Evolutionary Variational Inequalities


Stefan Reitmann

Freiberg University of Mining and Technology,
Institute of Computer Science, Germany
Chair of Virtual Reality and Multimedia
Doctor of Engineering
Technological University Bergakademie Freiberg
Akademiestrasse 6
09599 Freiberg,Germany

Bernhard Jung

Freiberg University of Mining and Technology,
Institute of Computer Science,Geremany
Chair of Virtual Reality and Multimedia
Doctor of Science
Technological University Bergakademie Freiberg
Akademiestrasse 6
09599 Freiberg,

Elena V. Kudryashova

Department of Applied Cybernetics,
St. Petersburg State University
Doctor of Physical and Mathematical Sciences,
Leading Researcher
198504 St.Peterburg Starii Petergof
Universitetski pr.28

Volker Reitmann

Department of Applied Cybernetics,
St. Petersburg State University
Doctor of Physical and Mathematical Sciences,
198504 St.Peterburg Starii Petergof
Universitetski pr.28


We derive absolute observation stability and instability results for controlled evolutionary inequalities which are based on frequency-domain characteristics of the linear part of the inequalities. The uncertainty parts of the inequalities (nonlinearities which represent external forces and constitutive laws) are described by certain local and integral quadratic constraints. Other terms in the considered evolutionary inequalities represent contact-type properties of a mechanical system with dry friction. The absolute stability criteria with respect to a class of observation operators (or measurement operators) gives the opportunity to prove the weak convergence of arbitrary solutions of inequalities to their stationary sets. In particular the obtained results can be used for the investigation of continuum type memories in neural networks. In such a way we can introduce a new type of neurons with hysteretic nonlinearities which are described by evolutionary variational inequalities.



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