Construction of a set of differerntial equations systems and stability in the vicinity of a program manifold

Authors

DOI:

https://doi.org/10.26577/JMMCS2024-v123-i3-6
        57 84

Keywords:

absolute stability, program manifold, indirect automatic control systems, Lyapunov function, Lurie-Letov type system

Abstract

 The problem of constructing a entire set of differential equation systems for a given program manifold is addressed. Necessary and sufficient conditions have been compiled to ensure that the program manifold is integral to the systems being developed. These conditions form a rectangular linear algebraic system in relation to the required functions. Using the property of a rectangular
matrix, the set of differential equation systems was constructed. Additionally, the problem of designing indirect automatic control systems with rigid feedback is explored. Since the given program is not always executed perfectly due to initial or ongoing disturbances, it is reasonable to require stability of the program manifold with respect to a certain function. This leads to the analysis of the stability of the system of equations in relation to the given program manifold. Through the construction of Lyapunov functions for the system in canonical form, sufficient conditions for the absolute stability of the program manifold are derived. These results can be applied to the design of stable automatic indirect control systems.

Author Biographies

S.S. Zhumatov, Institute of Mathematics and Mathematical Modeling, Kazakhstan, Almaty

Zhumatov Sailaubay– Doctor of Physical and Mathematical Sciences, Chief Researcher of the Institute of Mathematics and Mathematical Modeling SC MSHE RK (Almaty, Kazakhstan, email: sailau.math@mail.ru)

Zh.M. Kadirbayeva, Institute of Mathematics and Mathematical Modeling, Kazakhstan, Almaty

Kadirbayeva Zhazira (corresponding author)– Candidate of Physical and Mathematical Sciences, Leading Researcher of the Institute of Mathematics and Mathematical Modeling SC MSHE RK; Associate Professor of the Mathematics Department at the Kazakh National Women’s Teacher Training University (Almaty, Kazakhstan, email: zhkadirbayeva@gmail.com)

Z.S. Kobeyeva, Shymkent University, Kazakhstan, Shymkent

Kobeyeva Zagira– PhD, head of the Mathematics and Computer Science department at the Shymkent University (Shymkent, Kazakhstan, email: kobeebazagi82@mail.ru)

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How to Cite

Zhumatov, S. ., Kadirbayeva, Z. ., & Kobeyeva, Z. . (2024). Construction of a set of differerntial equations systems and stability in the vicinity of a program manifold. Journal of Mathematics, Mechanics and Computer Science, 123(3), 48–56. https://doi.org/10.26577/JMMCS2024-v123-i3-6