Аннотация:
In this paper, the stability and stabilization problems for nonlinear Volterra integrodifferential equations with unlimited delay are considered. The development of the direct Lyapunov method in the study of the limiting properties of the solutions of these equations is carried out by using Lyapunov functionals with a semidefinite time derivative. The topological dynamics of these equations has been constructed revealing the limiting properties of their solutions. The assumption of the existence of a Lyapunov functional with a semidefinite time derivative gives a more complete solution to the positive limit set localization problem. On this basis new theorems on sufficient conditions for the asymptotic stability and instability of the zero solution of nonlinear Volterra integro-differential equations are proved. These theorems are applied to the problem of the equilibrium position stability of the hereditary mechanical systems as well as the regulation problem of the controlled mechanical systems using a proportional-integro-differential controller. As an example, the regulation problem of a mobile robot with three omnidirectional wheels and a displaced mass center is solved using the nonlinear integral controllers without velocity measurements.
This work was supported by the grant of the Ministry of Education and Science of Russia within the framework of the State task [9.5994.2017/BP] and the Russian Foundation for Basic Research [18-01-00702, 18-41-730022].
Поступила в редакцию: 14.05.2018 Принята в печать: 13.09.2018
Образец цитирования:
A. S. Andreev, O. A. Peregudova, “On the Stability and Stabilization Problems of Volterra Integro-Differential Equations”, Нелинейная динам., 14:3 (2018), 387–407
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Эта публикация цитируется в следующих 10 статьяx:
Azizbeck Akhmatov, Jamshid Buranov, Jumanazar Khusanov, Olga Peregudova, “Global Position Feedback Tracking Control of a Serial Robot Manipulator with Revolute Joints”, Syst. Theor. Control Comput. J., 2:1 (2022), 8
J. R. Graef, C. Tunc, H. Sevli, “Razumikhin qualitative analyses of Volterra integro-fractional delay differential equation with Caputo derivatives”, Commun. Nonlinear Sci. Numer. Simul., 103 (2021), 106037
M. Bohner, O. Tunc, C. Tunc, “Qualitative analysis of Caputo fractional integro-differential equations with constant delays”, Comput. Appl. Math., 40:6 (2021), 214
O. Tunc, O. Atan, C. Tunc, J.-Ch. Yao, “Qualitative analyses of integro-fractional differential equations with Caputo derivatives and retardations via the Lyapunov-Razumikhin method”, Axioms, 10:2 (2021), 58
Nguyen Thu Ha, “On the robust stability of Volterra differential-algebraic equations”, Syst. Control Lett., 149 (2021), 104883
Aleksandr Andreev, Olga Peregudova, Lecture Notes in Electrical Engineering, 695, CONTROLO 2020, 2021, 686
A. Andreev, O. Peregudova, “On output feedback stabilization and tracking control of elastic-joint robotic manipulators”, 2019 23rd International Conference on Mechatronics Technology (ICMT 2019), IEEE, 2019
A. S. Andreev, O. A. Peregudova, “Semi-definite Lyapunov functionals in the stability problem of Volterra integral-differential equations”, IFAC PAPERSONLINE, 52:18 (2019), 103–108
A. Andreev, O. Peregudova, “On time-delayed feedback trajectory tracking control of a mobile robot with omni-wheels”, 2019 12Th International Workshop on Robot Motion and Control (Romoco `19), International Workshop on Robot Motion and Control, IEEE, 2019, 143–147
Aleksandr Andreev, Olga Peregudova, 2019 12th International Workshop on Robot Motion and Control (RoMoCo), 2019, 143