Show/Hide Menu
Hide/Show Apps
Logout
Türkçe
Türkçe
Search
Search
Login
Login
OpenMETU
OpenMETU
About
About
Open Science Policy
Open Science Policy
Communities & Collections
Communities & Collections
Help
Help
Frequently Asked Questions
Frequently Asked Questions
Guides
Guides
Thesis submission
Thesis submission
MS without thesis term project submission
MS without thesis term project submission
Publication submission with DOI
Publication submission with DOI
Publication submission
Publication submission
Supporting Information
Supporting Information
General Information
General Information
Copyright, Embargo and License
Copyright, Embargo and License
Contact us
Contact us
Tikhonov theorem for differential equations with singular impulses
Download
index.pdf
Date
2018-01-01
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
31
views
0
downloads
Cite This
The paper considers impulsive systems with singularities. The main novelty of the present research is that impulses (impulsive functions) are singular. This is beside singularity of differential equations. The Lyapunov second method is applied to proof the main theorems. Illustrative examples with simulations are given to support the theoretical results.
Subject Keywords
Singular differential equations
,
Tikhonov theorem
,
Singular impulsive functions
,
Lyapunov second method
URI
https://hdl.handle.net/11511/38719
Journal
Discontinuity, Nonlinearity, and Complexity
DOI
https://doi.org/10.5890/dnc.2018.09.007
Collections
Department of Mathematics, Article
Suggestions
OpenMETU
Core
Discrete linear Hamiltonian systems: Lyapunov type inequalities, stability and disconjugacy criteria
Zafer, Ağacık (2012-12-15)
In this paper, we first establish new Lyapunov type inequalities for discrete planar linear Hamiltonian systems. Next, by making use of the inequalities, we derive stability and disconjugacy criteria. Stability criteria are obtained with the help of the Floquet theory, so the system is assumed to be periodic in that case.
Periodic solutions and stability of linear impulsive delay differential equations
ALZabut, Jehad; Ağacık, Zafer; Department of Mathematics (2004)
In this thesis, we investigate impulsive differential systems with delays of the form And more generally of the form The dissertation consists of five chapters. The first chapter serves as introduction, contains preliminary considerations and assertions that will be encountered in the sequel. In chapter 2, we construct the adjoint systems and obtain the variation of parameters formulas of the solutions in terms of fundamental matrices. The asymptotic behavior of solutions of systems satisfying the Perron co...
Boundary value problems for higher order linear impulsive differential equations
Uğur, Ömür; Akhmet, Marat; Taşeli, Hasan; Department of Mathematics (2003)
The theory of impulsive di®erential equations has become an important area of research in recent years. Linear equations, meanwhile, are fundamental in most branches of applied mathematics, science, and technology. The theory of higher order linear impulsive equations, however, has not been studied as much as the cor- responding theory of ordinary di®erential equations. In this work, higher order linear impulsive equations at xed moments of impulses together with certain boundary conditions are investigated...
Global exponential stability of neural networks with non-smooth and impact activations
Akhmet, Marat (2012-10-01)
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant argument. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant argument of generalized type. Sufficient conditions ensuring the existence, uniqueness and global exponential stability of the equilibrium point are obtained. By employing Green's function we derive new result of existence of the periodic solution. The global exponential s...
Discrete event supervisor design and application for manufacturing systems with arbitrary faults and repairs
Acar, Ayşe Nur; Schmidt, Klaus Verner (2015-10-07)
This paper considers the supervisory control of discrete event systems (DES) that are subject to faults. To this end, an existing method for the fault-recovery and repair of single faults is extended to the case of different faults. As a result, we obtain a supervisor that follows the specified nominal system behavior in the fault-free case, converges to a desired degraded behavior for each fault type and recovers the nominal behavior after repair. The results of the paper are illustrated by a small example.
Citation Formats
IEEE
ACM
APA
CHICAGO
MLA
BibTeX
M. Akhmet, “Tikhonov theorem for differential equations with singular impulses,”
Discontinuity, Nonlinearity, and Complexity
, pp. 291–303, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38719.