Displaying similar documents to “An analysis on the stability of a state dependent delay differential equation”

On delay-dependent stability for neutral delay-differential systems

Qing-Long Han (2001)

International Journal of Applied Mathematics and Computer Science

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This paper deals with the stability problem for a class of linear neutral delay-differential systems. The time delay is assumed constant and known. Delay-dependent criteria are derived. The criteria are given in the form of linear matrix inequalities which are easy to use when checking the stability of the systems considered. Numerical examples indicate significant improvements over some existing results.

On delay-dependent robust stability under model transformation of some neutral systems

Salvador A. Rodríguez, Luc Dugard, Jean-Michel Dion, Jesús de León (2009)

Kybernetika

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This paper focuses on the delay-dependent robust stability of linear neutral delay systems. The systems under consideration are described by functional differential equations, with norm bounded time varying nonlinear uncertainties in the "state" and norm bounded time varying quasi-linear uncertainties in the delayed "state" and in the difference operator. The stability analysis is performed via the Lyapunov-Krasovskii functional approach. Sufficient delay dependent conditions for robust...

Delays induced in population dynamics

Eva Sánchez (2003)

Banach Center Publications

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This paper provides an introduction to delay differential equations together with a short survey on state-dependent delay differential equations arising in population dynamics. Our main goal is to examine how the delays emerge from inner mechanisms in the model, how they induce oscillations and stability switches in the system and how the qualitative behaviour of a biological model depends on the form of the delay.

Delay-dependent asymptotic stabilitzation for uncertain time-delay systems with saturating actuators

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.

Delay differential systems with time-varying delay: new directions for stability theory

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...

Stability and Boundedness of Solutions of Some Third-order Nonlinear Vector Delay Differential Equation

Larbi Fatmi, Moussadek Remili (2016)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

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This paper investigates the stability of the zero solution and uniformly boundedness and uniformly ultimately boundedness of all solutions of a certain vector differential equation of the third order with delay. Using the Lyapunov–Krasovskiĭ functional approach, we obtain a new result on the topic and give an example for the related illustrations.

Stabilization of solutions to a differential-delay equation in a Banach space

J. J. Koliha, Ivan Straškraba (1997)

Annales Polonici Mathematici

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A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.