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
Differential Equations – Springer Journals
Published: Mar 14, 2018
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