Stability and Asymptotic Behavior for Certain Systems of Delay Difference Equations
J. Morchało (1997)
Publications de l'Institut Mathématique
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J. Morchało (1997)
Publications de l'Institut Mathématique
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James Louisell (2001)
Kybernetika
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In this paper we give an example of Markus–Yamabe instability in a constant coefficient delay differential equation with time-varying delay. For all values of the range of the delay function, the characteristic function of the associated autonomous delay equation is exponentially stable. Still, the fundamental solution of the time-varying system is unbounded. We also present a modified example having absolutely continuous delay function, easily calculating the average variation of the...
A. F. Ivanov (1989)
Banach Center Publications
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M. Calvo, T. Grande (1989)
Numerische Mathematik
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Sokhadze, Z. (1995)
Memoirs on Differential Equations and Mathematical Physics
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Sertaç Erman, Ali Demir (2016)
Open Mathematics
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In this paper, we present an analysis for the stability of a differential equation with state-dependent delay. We establish existence and uniqueness of solutions of differential equation with delay term [...] τ(u(t))=a+bu(t)c+bu(t). Moreover, we put the some restrictions for the positivity of delay term τ(u(t)) Based on the boundedness of delay term, we obtain stability criterion in terms of the parameters of the equation.
Pin-Lin Liu (2005)
International Journal of Applied Mathematics and Computer Science
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This paper concerns the issue of robust asymptotic stabilization for uncertain time-delay systems with saturating actuators. Delay-dependent criteria for robust stabilization via linear memoryless state feedback have been obtained. The resulting upper bound on the delay time is given in terms of the solution to a Riccati equation subject to model transformation. Finally, examples are presented to show the effectiveness of our result.
Abbes Benaissa, Mostefa Miloudi, Mokhtar Mokhtari (2015)
Commentationes Mathematicae Universitatis Carolinae
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We consider the Bresse system in bounded domain with delay terms in the internal feedbacks and prove the global existence of its solutions in Sobolev spaces by means of semigroup theory under a condition between the weight of the delay terms in the feedbacks and the weight of the terms without delay. Furthermore, we study the asymptotic behavior of solutions using multiplier method.
Sonnenberg, Amnon, Crain, Bradford R. (2005)
Journal of Theoretical Medicine
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J. Džurina (1997)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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Our aim in this paper is to present the relationship between property (B) of the third order equation with delay argument y'''(t) - q(t)y(τ(t)) = 0 and the oscillation of the second order delay equation of the form y''(t) + p(t)y(τ(t)) = 0.