https://doi.org/10.1140/epjs/s11734-025-02032-w
Regular Article
Stabilization of nonlinear mechanical systems via homogeneous delayed feedback
Faculty of Applied Mathematics and Control Processes, Saint Petersburg State University, 7-9 Universitetskaya Nab., 199034, Saint Petersburg, Russia
Received:
16
December
2024
Accepted:
17
October
2025
Published online:
29
October
2025
The stabilization problem for a nonlinear holonomic mechanical system is studied. To provide the asymptotic stability of the trivial equilibrium position, a PID controller is used. An original construction of complete-type Lyapunov–Krasovskii functional for the closed-loop system is proposed. With the aid of this functional, stabilization conditions and estimates of the convergence rate of solutions to the equilibrium position are derived. The developed approach is applied to the problem of monoaxial stabilization of a rigid body via a control with delayed feedback.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
