Periodic motions generated from non-autonomous grazing dynamics

This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are stationary, and this makes necessity to study the problem in a new way. The models play exceptionally important role in mechanics and electronics. A concise review on the sufficient conditions for the new type of linearization is presented. The existence and stability of periodic solutions are considered under the circumstance of the regular perturbation. To visualize the theoretical results, mechanical examples are presented.


Stability in non-autonomous periodic systems with grazing stationary impacts
Akhmet, Marat (2017-01-01)
This paper examines impulsive non-autonomous periodic systems whose surfaces of discontinuity and impact functions are not depending on the time variable. The W-map which alters the system with variable moments of impulses to that with fixed moments and facilitates the investigations, is presented. A particular linearizion system with two compartments is utilized to analyze stability of a grazing periodic solution. A significant way to keep down a singularity in linearizion is demonstrated. A concise review...
Frequency-domain subspace identification of linear time-periodic (LTP) systems
Uyanık, İsmail; Saranlı, Uluç; Ankaralı, Mustafa Mert; Cowan, Noah J.; Morgül, Ömer (Institute of Electrical and Electronics Engineers (IEEE), 2019-06)
This paper proposes a new methodology for subspace-based state-space identification for linear time-periodic (LTP) systems. Since LTP systems can be lifted to equivalent linear time-invariant (LTI) systems, we first lift input-output data from an unknown LTP system as if they were collected from an equivalent LTI system. Then, we use frequency-domain subspace identification methods to find the LTI system estimate. Subsequently. we propose a novel method to obtain a time-periodic realization for the estimate...
Stability criteria for linear periodic impulsive Hamiltonian systems
Guseinov, G. Sh.; Zafer, Ağacık (2007-11-15)
In this paper we obtain stability criteria for linear periodic impulsive Hamiltonian systems. A Lyapunov type inequality is established. Our results improve also the ones previously obtained for systems without impulse effect. (c) 2007 Elsevier Inc. All rights reserved.
Non-autonomous grazing phenomenon
Akhmet, Marat (2017-02-01)
Non-autonomous grazing phenomenon is investigated through periodic systems and their solutions. The analysis is different than for autonomous systems in many aspects. Conditions for the existence of a linearization have been found. Stability of a periodic solution and its persistence under regular perturbations are investigated. Through examples, the theoretical results are visualized.
Almost Periodic Solutions of Recurrent Neural Networks with State-Dependent and Structured Impulses
Akhmet, Marat; Erim, Gülbahar (2023-01-01)
The subject of the present paper is recurrent neural networks with variable impulsive moments. The impact activation functions are specified such that the structure for the jump equations are in full accordance with that one for the differential equation. The system studied in this paper covers the works done before, not only because the impacts have recurrent form, but also impulses are not state-dependent. The conditions for existence and uniqueness of asymptotically stable discontinuous almost periodic s...
Citation Formats
M. Akhmet, “Periodic motions generated from non-autonomous grazing dynamics,” COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, pp. 48–62, 2017, Accessed: 00, 2020. [Online]. Available: