On stability and stabilization of motion with respect to a part of the variables / Vorotnikov V.I. // Journal of Applied Mathematics and Mechanics. - 1982. - V. 46, l. 6. - P. 733-740.

ISSN:

00218928

Type:

Article

Abstract:

The method of Liapunov vector function is used to obtain the conditions of stability and instability of motion of a system with respect to a part of its variables. The system is described by ordinary differential equations with continuous right-hand sides. A technique for the solution of the problem concerning the stabilization of motion with respect to a part of the variables is discussed. This technique enables one to take into account the requirements previously specified, regarding the nature of the transition processes of the system, and to solve partially the problem of minimizing the demand on resources. A discussion is also presented of a method for the solution of minimization of a functional and of a game theoretic problem on a minimax-maximin of a functional, with the aim of satisfying the prescribed requirements regarding the nature of the transition processes with respect to a part of the variables in the initial system. Mechanical examples are solved. © 1983.

Author keywords:

Index keywords:

CONTROL, MECHANICAL VARIABLES; MATHEMATICAL TECHNIQUES - Differential Equations; SYSTEM STABILITY

DOI:

10.1016/0021-8928(82)90053-3

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-0020224793&doi=10.1016%2f0021-8928%2882%2990053-3&partnerID=40&md5=74eb8eb58f794c29a9e46188f8558394

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References	Rumiantsev, On the stability of motion with respect to a part of the variables (1957) Vestn. MGU, Matem., Mekhan., (4); See also L.-N.Y. Acad. Press, 1971; Oziraner, Rumiantsev, The method of Liapunov functions in the stability problem for motion with respect to a part of the variables (1972) PMM, 36 (2); Vorotnikov, Prokop'ev, On stability of motion of linear systems with respect to a part of variables (1978) PMM, 42 (2); Vorotnikov, On the stability of motion relative to part of the variables for certain nonlinear systems (1979) PMM, 43 (3); Matrosov, The principle of comparison with the Liapunov vector function (1969) IV. Differents. uravneniia, 5 (12); Wazewski, Systémès des équations et des inéqua différentielles ordinaires aux deuxièmes membres monotones et leurs applications (1950) Ann. Soc. Polon. Math., 23; Chetaev, (1961) Stability of Motion, , Pergamon Press, Book No. 09505; Rumiantsev, On asymptotic stability and instability of motion with respect to a part of the variables (1971) PMM, 35 (1); Rumiantsev, On the stability with respect to a part of the variables (1971) Sympos. Math., 6. , Meccanica nonlineare e stabilita, Acad. Press, London-New York; Rumiantsev, On the optimal stabilization of controlled systems (1970) PMM, 34 (3); Vorotnikov, On the stability and stabilization of motion with respect to a part of the variables, for the linear systems with delay (1980) Avtomatika i telemekhanika, (8); Vorotnikov, On the complete controllability and stabilization of motion with respect to a part of the variables (1982) Avtomatika i telemekhanika, (3); Krasovskii, Problem of stabilization of controlled motions (1966) Theory of Stability of Motion, , I.G. Malkin, NAUKA, Moscow; Bodner, (1964) Theory of Automatic Control of Flight, , NAUKA, Moscow; Repin, Tret'iakov, Solution of the problem of analytic construction of regulators for the electornic modelling devices (1963) Avtomatika i telemekhanika, 24; Letov, (1969) Dynamics of flight and its control, , NAUKA, Moscow; Krasovskii, Subbotin, (1974) Positional Differential Games, , NAUKA, Moscow
CODEN	JAMMA
Language of Original Document	English
Abbreviated Source Title	J. Appl. Math. Mech.
Source	Scopus