OPTIMAL STABILIZATION IN DIFFERENCE EQUATIONS
DOI:
https://doi.org/10.17721/2706-9699.2024.1.05Keywords:
optimal stabilization, difference equations, Lyapunov functions, optimal controlAbstract
The paper deals with the problem of optimal stabilization for difference equations. The use of Lyapunov functions for optimal stabilization is discussed. The theorem of optimal stabilization is proved and the form of optimal control for the considered class of problems is determined.
References
Malkin I.G. Theory of stability of motion. M.: Nauka, 1966. 532 p.
Halanai A., Wexler D. Qualitative theory of impulse systems. Mir Publishing House, Moscow, 1971. 309 p.
Martyniuk D.I. Lectures on the qualitative theory of difference equations. Kyiv: Naukova Dumka. 1972. 246 p.
Rusch N, Abets P, Lalois M. The direct Lyapunov method in stability theory. Mir Publishing House, Moscow, 1980. 300 p.
Slyusarchuk V.Yu. Stability of solutions of differential equations in Banach space. Rivne: UDUVHP Publishing House, 2003. 366 p.
Demchenko H., Diblik J., Khusainov D.Ya. Optimal stabilization for differential systems with delays – Malkin’s approach. Journal of the Franklin Institute. 356(9), 4811-4841. https://doi.org/10.1016/j.jfranklin.2019.04.021
Martyniuk A.A., Chernienko V.O. On the stabilization of the motion of non-autonomous polynomial systems. Applied mechanics. Vol. 57. No. 5. P. 35-45.
Martyniuk A.A., Khusainov D.Ya., Chernyenko V.A. Constructive estimation of the Lyapunov function for systems with quartic nonlinearity. Applied mechanics. 2018. Vol. 54(64). No. 3. P. 114-126.
Matvienko V.T., Pichkur V.T., Cherny D.I., Demkivskyi E.O. General solution of the problem of terminal control of a linear discrete system. Journal of Numerical and Applied Mathematics. 2022. No. 2. P. 83-90. https://doi.org/10.17721/2706-9699.2022.2.10
Husainov D.Ya., Shatyrko A.V., Gagurin E.R. Optimal stabilization in differential equations. Journal of Numerical and Applied Mathematics. 2022. No. 2. P. 158-164. https://doi.org/10.17721/2706-9699.2022.2.18
Husainov D.Ya., Shatyrko A.V., Gagurin E.R. Optimal stabilization in systems of differential equations. Bulletin of the National Technical University "KhPI". Series "Mathematical modeling in engineering and technology". 2023. No. 1. P. 205-211.
