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List of publications on a keyword: «stability theory»

  • Sovremennye problemy teorii ustoichivosti i soderzhanie kursa matematiki v tekhnicheskom vuze

    Book Chapter
    Psychological and Pedagogical Issues of Modern Education
    Authors:
    Olga G. Antonovskaia, Antonina V. Besklubnaia
    Work direction:
    Chapter 1
    Abstract:
    This paper addresses the problem of the "Stability reserve" issue in the "Stability theory" section in the system dynamics, differential equations and other courses for students of technical specialties. The problems of stability reserve determination are examined first of all from the point of view of accessibility of material account and possibility of its practical use when solving applied problems on the base of knowledge obtained by the students of technical high educational institutions in mathematical courses.
    Keywords:
    professional activity of the trainee, fundamentals of education, ability to construct models of real phenomena, mathematical methods of research, stability theory, robust stability, stability reserve
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  • Priamoi metod Liapunova i ego izlozhenie v sovremennom uchebnom protsesse

    Book Chapter
    Education and science: current trends
    Authors:
    Olga G. Antonovskaia, Antonina V. Besklubnaia
    Work direction:
    Глава 1. Теоретические аспекты образования
    Abstract:
    The article is devoted to the problem of the full treatment of the subject “Construction of Lyapunov functions” in the “Lyapunov's direct method” section in the courses on system dynamics, differential equations, etc., for students of mathematical and technical specialties. The authors of the article point out that first of all Lyapunov function method is considered the method useful for studying dynamics of concrete technical systems by mathematical methods. Since for practical use of this method it makes sense to construct Lyapunov functions in simplest form, the methodology for constructing Lyapunov functions in positive definite quadratic forms with given properties, certain features of original problems is proposed by the authors.
    Keywords:
    professional activity of the trainee, fundamentals of education, professionally significant and practical goals of education, ability to construct models of real phenomena, mathematical methods of research, stability theory, Lyapunov's direct method, positive definite quadratic form, Lyapunov matrix equation
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