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

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

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Global Problems of Differential Inclusions: the Problems of Kalman and Vyshnegradskii, Chua's Circuit

Author(s):

G. A. Leonov

Saint-Petersburg State University
Mathematics and Mechanics Faculty
Department of Applied Cybernetics
Professor, Head of Department
Dr. of Science
Universitetsky prospekt, 28
St.-Petersburg, Petrodvoretz,198504, RUSSIA

leonov@math.spbu.ru

N. V. Kuznetsov

Saint-Petersburg State University
Mathematics and Mechanics Faculty
Department of Applied Cybernetics
Professor, Deputy Head of Department
PhD,Dr. of Science
Universitetsky prospekt, 28
St.-Petersburg, Petrodvoretz,198504, RUSSIA

nkuznetsov239@gmail.com

M. A. Kiseleva

Saint-Petersburg State University
Mathematics and Mechanics Faculty
Department of Applied Cybernetics
PhD, Leading Researcher
Universitetsky prospekt, 28
St.-Petersburg, Petrodvoretz,198504, RUSSIA

maria.kiseleva.87@gmail.com

R. N. Mokaev

Saint-Petersburg State University
Mathematics and Mechanics Faculty
Department of Applied Cybernetics
Junior Researcher
Universitetsky prospekt, 28
St.-Petersburg, Petrodvoretz,198504, RUSSIA

r.mokaev@spbu.ru

Abstract:

This paper describes various approaches to determine the solutions of differential equations with discontinuous right side and differential inclusions. For discontinuous systems within the classical Vyshnegradskii problem the Lyapunov discontinuous functions are applied. To construct counterexamples to the Kalman conjecture for smooth systems the discontinuous approximation method and the ideas of Aizerman and Pyatnitskii are applied.

Keywords

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