Stability criteria for linear periodic impulsive Hamiltonian systems

Guseinov, G. Sh.
Zafer, Ağacık
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.
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.
On periodic solutions of linear impulsive delay differential systems
Akhmet, Marat; Alzabut, J.O.; Zafer, Ağacık (2008-10-01)
A necessary and sufficient condition is established for the existence of periodic solutions of linear impulsive delay differential systems. Copyright © 2008 Watam Press.
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...
Almost periodic solutions of the linear differential equation with piecewise constant argument
Akhmet, Marat (2009-10-01)
The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Citation Formats
G. S. Guseinov and A. Zafer, “Stability criteria for linear periodic impulsive Hamiltonian systems,” JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, pp. 1195–1206, 2007, Accessed: 00, 2020. [Online]. Available: