M. A. Aizerman, Ye. S. Pyatnitskii, “Fundamentals of the theory of discontinuous systems. I”, Avtomat. i Telemekh., 1974, no. 7, 33

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Avtomatika i Telemekhanika, 1974, Issue 7, Pages 33–47 (Mi at8429)

This article is cited in 10 scientific papers (total in 10 papers)

Discrete Systems

Fundamentals of the theory of discontinuous systems. I

M. A. Aizerman, Ye. S. Pyatnitskii

Moscow

Full-text PDF (2902 kB) Citations (10)

Abstract: A general theory of discontinuous systems is studied in connection with the theory of relay systems, variable-structure systems, synthesis of optimal control laws and the theory of some other discontinuous systems. The first part of the paper introduces definition of a solution for a discontinuous system and shows that by this definition all basic properties of solutions of differential equations with a continuous right-hand part (except uniqueness) are generalized to discontinuous systems. In the second part it is shown how this definition can lead to completeness of definition of a discontinuous problem in all points of the discontinuity surfaces and in their intersection points.

Received: 01.01.1974

Document Type: Article

UDC: 62-50:519.2

Language: Russian

Citation: M. A. Aizerman, Ye. S. Pyatnitskii, “Fundamentals of the theory of discontinuous systems. I”, Avtomat. i Telemekh., 1974, no. 7, 33–47

Citation in format AMSBIB

\Bibitem{1}

\by M. A. Aizerman, Ye. S. Pyatnitskii

\paper Fundamentals of the theory of discontinuous systems. I

\jour Avtomat. i Telemekh.

\yr 1974

\issue 7

\pages 33--47

\mathnet{http://mi.mathnet.ru/at8429}

Linking options:

https://www.mathnet.ru/eng/at8429

https://www.mathnet.ru/eng/at/y1974/i7/p33

This publication is cited in the following 10 articles:

Kuznetsov V N., “Theory of Hidden Oscillations and Stability of Control Systems”, J. Comput. Syst. Sci. Int., 59:5 (2020), 647–668
I. L. Kirilyuk, “Diskretnaya forma uravnenii v teorii pereklyuchayuschegosya vosproizvodstva s razlichnymi variantami finansovykh potokov”, Kompyuternye issledovaniya i modelirovanie, 8:5 (2016), 803–815
M. M. Živanović, M. P. Lazarević, “Using the decomposition principle to stabilize the nominal motion of a mechanical system with given accuracy”, Autom. Remote Control, 73:12 (2012), 2001–2020
I. A. Finogenko, “On differential inclusions with additive generalized functions”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S85–S94
S. A. Kochetkov, V. A. Utkin, “Compensating unremovable imperfections in operation units”, Autom. Remote Control, 71:5 (2010), 747–771
O. V. Morzhin, “Nonlocal improvement of nonlinear controlled processes on the basis of sufficient optimality conditions”, Autom. Remote Control, 71:8 (2010), 1526–1539
I. A. Finogenko, “O differentsialnykh uravneniyakh s razryvnoi pravoi chastyu”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 3:2 (2010), 88–102
S. A. Kochetkov, S. A. Krasnova, V. A. Utkin, “Metod regulyarizatsii skolzyaschikh dvizhenii po obratnoi svyazi”, Ufimsk. matem. zhurn., 1:4 (2009), 67–77
V. N. Zhermolenko, “Periodic motions and criteria of absolute stability, instability, and controllability of two-dimensional bilinear systems”, Autom. Remote Control, 67:8 (2006), 1194–1214
I. V. Matrosov, “Existence of solutions of the algebro-differential equations”, Autom. Remote Control, 67:9 (2006), 1408–1415

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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