Sur la stabilité asymptotique de la solution d'un système d'équations différentielles à paramètre retardé
Switching signal design for global exponential stability of uncertain switched neutral systems.
The method of averaging and functional differential equations with delay.
The method of Lyapunov functionals for neutral-type linear difference-differential systems with almost-periodic coefficients.
The Region of Attraction of the Zero Solution of y' (t) = - (y(t-1)) 2m+1.
Total stability in abstract functional differential equations with infinite delay.
Tracking with prescribed transient behaviour
Universal tracking control is investigated in the context of a class of -input, -output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal of class (absolutely...
Tracking with prescribed transient behaviour
Universal tracking control is investigated in the context of a class S of M-input, M-output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains – as a prototype subclass – all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary -valued reference signal r of class W1,∞ (absolutely...
Ultimate boundedness of some third order ordinary differential equations
We prove the ultimate boundedness of solutions of some third order nonlinear ordinary differential equations using the Lyapunov method. The results obtained generalize earlier results of Ezeilo, Tejumola, Reissig, Tunç and others. The Lyapunov function used does not involve the use of signum functions as used by others.
Une remarque sur l'évaluation de la région d'attraction de la solution banale d'un système d'équations différentielles piloté avec le paramètre retardé
Uniform exponential stability of linear almost periodic systems in Banach spaces.
Uniform exponential stability of linear periodic systems in a Banach space.
Uniform Stability In Nonlinear Infinite Delay Volterra Integro-differential Equations Using Lyapunov Functionals
In [10] the first author used Lyapunov functionals and studied the exponential stability of the zero solution of finite delay Volterra Integro-differential equation. In this paper, we use modified version of the Lyapunov functional that were used in [10] to obtain criterion for the stability of the zero solution of the infinite delay nonlinear Volterra integro-differential equation [...]
Viral infection model with diffusion and state-dependent delay: a case of logistic growth
We propose a virus dynamics model with reaction-diffusion and logistic growth terms, intracellular state-dependent delay and a general non-linear infection rate functional response. Classical solutions with Lipschitz in-time initial functions are investigated. This type of solutions is adequate to the discontinuous change of parameters due to, for example, drug administration. The Lyapunov functions approach is used to analyse stability of interior infection equilibria which describe the cases of...
Viral in-host infection model with two state-dependent delays: stability of continuous solutions
A virus dynamics model with two state-dependent delays and logistic growth term is investigated. A general class of nonlinear incidence rates is considered. The model describes the in-host interplay between viral infection and CTL (cytotoxic T lymphocytes) and antibody immune responses. The wellposedness of the model proposed and Lyapunov stability properties of interior infection equilibria which describe the cases of a chronic disease are studied. We choose a space of merely continuous initial...
Асимптотическая устойчивость системы дифференциальных уравнений с последействием, содержащих малый параметр
Критерий устойчивости систем с запаздыванием в одном критическом случае
О сведении устойчивого уравнения нейтрального типа к уравнению запаздывающего типа
Об одном подходе к исследованию устойчивости периодических решений в принципе усреднения для функционально-дифференциальных уравнений нейтрального типа
Об оценке и устойчивости решений дифференциальных уравнений с запаздыванием в Банаховом пространстве