Stability in non-autonomous periodic systems with grazing stationary impacts

Date

2017-01-01

Author

Akhmet, Marat

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

194
views

0
downloads

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 on sufficient conditions for the linearizion and stability is presented. An example is given to actualize the theoretical results.

Subject Keywords

Linearization of a non-autonomous system with grazing impacts, Stationary impact, Grazing impulse

URI

https://hdl.handle.net/11511/54367

Journal

CARPATHIAN JOURNAL OF MATHEMATICS

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

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.
Stability criteria for linear Hamiltonian systems under impulsive perturbations Kayar, Z.; Zafer, Ağacık (2014-03-01) Stability criteria are given for planar linear periodic Hamiltonian systems with impulse effect by making use of a Lyapunov type inequality. A disconjugacy criterion is also established. The results improve the related ones in the literature for such systems.
Periodic motions generated from non-autonomous grazing dynamics Akhmet, Marat (2017-08-01) 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 p...
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...
STABILITY OF CONTROL FORCES IN REDUNDANT MULTIBODY SYSTEMS IDER, SK (1996-01-03) In this paper inverse dynamics of redundant multibody systems using a minimum number of control forces is formulated. It is shown that the control forces and the task accelerations may become noncausal at certain configurations, yielding the dynamical equation set of the system to be singular. For a given set of tasks, each different set of actuators leads to a different system motion and also to different singular configurations. To avoid the singularities in the numerical solution, the dynamical equations...

Citation Formats

M. Akhmet, “Stability in non-autonomous periodic systems with grazing stationary impacts,” CARPATHIAN JOURNAL OF MATHEMATICS, pp. 1–8, 2017, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54367.