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This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable,…
In this work characterizations of notions of output stability for uncertain time-varying systems described by retarded functional differential equations are provided. Particularly, characterizations by means of Lyapunov and Razumikhin…
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
It is difficult to analyze the stability of systems with time-varying delays. One approach is to construct a time-transformation that converts the system into a form with a constant delay but with a time-varying scalar appearing in the…
In this article, we introduce Lyapunov-type results to investigate the stability of the trivial solution of a Stieltjes dynamical system. We utilize prolongation results to establish the global existence of the maximal solution. Using…
Large time behavior of solutions to abstract differential equations is studied. The corresponding evolution problem is: $$\dot{u}=A(t)u+F(t,u)+b(t), \quad t\ge 0; \quad u(0)=u_0. \qquad (*)$$ Here $\dot{u}:=\frac {du}{dt}$, $u=u(t)\in H$,…
We study the well-posedness of nonautonomous nonlinear delay equations in $\mathbb{R}^{n}$ as evolutionary equations in a proper Hilbert space. We present a construction of solving operators (nonautonomous case) or nonlinear semigroups…
In this paper, we consider the Kirchhoff plate equation with delay terms on the boundary control are added (see system \eqref{p5-2.1} below). we give some instability examples of system \eqref{p5-2.1} for some choices of delays. Finally, we…
This paper considers linear functional equations on $\mathbb R^d$ with distributed delays defined by matrix-valued measures of bounded variation. More precisely, we are interested in providing conditions to ensure that the exponential…
We study in this paper a forward-backward-forward dynamical system for solving a mixed variational inequality problem in a real Hilbert space. For the convergence analysis of our proposed system, we apply the Lyapunov analysis to obtain the…
This paper studies the problem of stability of a parameterized delay differential equations (DDE see equation (0.1)). After discretizing the DDE (0.1), we show that the problem can be equivalently casted into a semi-definite programming…
A deformation of the standard prolongation operation, defined on sets of vector fields in involution rather than on single ones, was recently introduced and christened "\sigma-prolongation"; correspondingly one has "\sigma-symmetries" of…
In this article, we propose a Lyapunov stability approach to analyze the convergence of the density operator of a quantum system. In contrast to many previously studied convergence analysis methods for invariant density operators which use…
For the nonlinear second order Lienard-type equations with time-varying delays $$ \ddot{x}(t)+\sum_{k=1}^m f_k(t,x(t),\dot{x}(g_k(t)))+\sum_{k=1}^l s_k(t,x(h_k(t)))=0, $$ global asymptotic stability conditions are obtained. The results are…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
The paper is devoted to the study of stability of equilibrium solutions of a delay differential equation that models leukemia. The equation was previously studied in [5] and [6], where the emphasis is put on the numerical study of periodic…
We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…
A proper discretization of the logistic differential equation, which is preserving these two distinct equilibrium solutions and their unstability and stability, suggest that we need to examine the time delay of the logistic map. According…
Several results regarding the stability and the stabilization of linear impulsive positive systems under arbitrary, constant, minimum, maximum and range dwell-time are obtained. The proposed stability conditions characterize the pointwise…