Global Problems for Differential Inclusions. Kalman and Vyshnegradskii Problems and Chua Circuits

Global Problems for Differential Inclusions. Kalman and Vyshnegradskii Problems and Chua Circuits ISSN 0012-2661, Differential Equations, 2017, Vol. 53, No. 13, pp. 1671–1702.  Pleiades Publishing, Ltd., 2017. CONTROL THEORY Global Problems for Differential Inclusions. Kalman and Vyshnegradskii Problems and Chua Circuits G. A.Leonov, N.V.Kuznetsov , M.A.Kiseleva, and R.N.Mokaev Saint Petersburg State University, St. Petersburg, 199034 Russia University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, 40014 Finland e-mail: nkuznetsov239@gmail.com DOI: 10.1134/S0012266117130018 1. INTRODUCTION The emergence of the theory of differential inclusions is usually associated with works by French mathematician A. Marchaud [1,2] and Polish mathematician S.K. Zaremba [3,4]. However, the de- velopment of the theory of differential inclusions was furthered not only by the research in the field of abstract mathematics but also by the studies of particular problems in mechanics (plasticity, dry friction, control with relay elements, tribology, etc.; see, for example, [5–33]). That is to say, along with general considerations and attempts to understand how the notion of derivative is introduced for differential inclusions, there were other trends, related to particular needs of applied problems. First, let us describe this concrete research and then switch to the general definitions of solutions to differential inclusions. In what follows, we consider the classical Vyshnegradskii and Kalman problems and prove theorems on http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Global Problems for Differential Inclusions. Kalman and Vyshnegradskii Problems and Chua Circuits

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Publisher
Pleiades Publishing
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
D.O.I.
10.1134/S0012266117130018
Publisher site
See Article on Publisher Site

Abstract

ISSN 0012-2661, Differential Equations, 2017, Vol. 53, No. 13, pp. 1671–1702.  Pleiades Publishing, Ltd., 2017. CONTROL THEORY Global Problems for Differential Inclusions. Kalman and Vyshnegradskii Problems and Chua Circuits G. A.Leonov, N.V.Kuznetsov , M.A.Kiseleva, and R.N.Mokaev Saint Petersburg State University, St. Petersburg, 199034 Russia University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, 40014 Finland e-mail: nkuznetsov239@gmail.com DOI: 10.1134/S0012266117130018 1. INTRODUCTION The emergence of the theory of differential inclusions is usually associated with works by French mathematician A. Marchaud [1,2] and Polish mathematician S.K. Zaremba [3,4]. However, the de- velopment of the theory of differential inclusions was furthered not only by the research in the field of abstract mathematics but also by the studies of particular problems in mechanics (plasticity, dry friction, control with relay elements, tribology, etc.; see, for example, [5–33]). That is to say, along with general considerations and attempts to understand how the notion of derivative is introduced for differential inclusions, there were other trends, related to particular needs of applied problems. First, let us describe this concrete research and then switch to the general definitions of solutions to differential inclusions. In what follows, we consider the classical Vyshnegradskii and Kalman problems and prove theorems on

Journal

Differential EquationsSpringer Journals

Published: Mar 14, 2018

References

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