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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

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 stability...

On delay-dependent stability for neutral delay-differential systems

Qing-Long Han (2001)

International Journal of Applied Mathematics and Computer Science

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 discreteness of spectrum of a functional differential operator

Sergey Labovskiy, Mário Frengue Getimane (2014)

Mathematica Bohemica

We study conditions of discreteness of spectrum of the functional-differential operator ℒ u = - u ' ' + p ( x ) u ( x ) + ∫ - ∞ ∞ ( u ( x ) - u ( s ) ) d s r ( x , s ) on ( - ∞ , ∞ ) . In the absence of the integral term this operator is a one-dimensional Schrödinger operator. In this paper we consider a symmetric operator with real spectrum. Conditions of discreteness are obtained in terms of the first eigenvalue of a truncated operator. We also obtain one simple condition for discreteness of spectrum.

On exponential stability of second order delay differential equations

Ravi P. Agarwal, Alexander Domoshnitsky, Abraham Maghakyan (2015)

Czechoslovak Mathematical Journal

We propose a new method for studying stability of second order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method...

On first order impulsive semilinear functional differential inclusions

Mouffak Benchohra, Johnny Henderson, Sotiris K. Ntouyas (2003)

Archivum Mathematicum

In this paper the Leray-Schauder nonlinear alternative for multivalued maps combined with the semigroup theory is used to investigate the existence of mild solutions for first order impulsive semilinear functional differential inclusions in Banach spaces.

On functional differential inclusions in Hilbert spaces

Myelkebir Aitalioubrahim (2012)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We prove the existence of monotone solutions, of the functional differential inclusion ẋ(t) ∈ f(t,T(t)x) +F(T(t)x) in a Hilbert space, where f is a Carathéodory single-valued mapping and F is an upper semicontinuous set-valued mapping with compact values contained in the Clarke subdifferential ∂ c V ( x ) of a uniformly regular function V.

Currently displaying 61 – 80 of 461