Abstract
The methodology of stability analysis is expounded to the systems automatic control feedback at presence of non-linearity. The conditions of asymptotically instability of the basic control systems are considered in the neighborhood of a program manifold. Nonlinearity satisfies to generalized conditions of local quadratic relations. The sufficient conditions of instability of the program manifold have been obtained relatively to a given vector-function by means of construction of Lyapunov function, in the form “quadratic form plus an integral from nonlinearity”. It is solved more general inverse problem of dynamics: not only builds the corresponding system of differential equations, but also investigates the instability, which is very important for a variety of mathematical models mechanics.
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Acknowledgements
This research is financially supported by a grant from the Ministry of Science and Education of the Republic of Kazakhstan (Grant No. 3357/GF4). This publication is supported by the target program 0085/PTSF-14 from the Ministry of Science and Education of the Republic of Kazakhstan.
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Zhumatov, S.S. (2017). On Instability of a Program Manifold of Basic Control Systems. In: Kalmenov, T., Nursultanov, E., Ruzhansky, M., Sadybekov, M. (eds) Functional Analysis in Interdisciplinary Applications. FAIA 2017. Springer Proceedings in Mathematics & Statistics, vol 216. Springer, Cham. https://doi.org/10.1007/978-3-319-67053-9_42
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DOI: https://doi.org/10.1007/978-3-319-67053-9_42
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