Related papers: Asymptotic properties of neutral type linear syste…
Exponential stability of the second order linear delay differential equation in $x$ and $u$-control $$ \ddot{x}(t)+a_1(t)\dot{x}(h_1(t))+a_2(t)x(h_2(t))+a_3(t)u(h_3(t))=0 $$ is studied, where indirect feedback control…
Asymptotic properties of solutions of difference equation of the form \[ \Delta^m(x_n+u_nx_{n+k})=a_nf(n,x_{\sigma(n)})+b_n \] are studied. We give sufficient conditions under which all solutions, or all solutions with polynomial growth, or…
In this paper, we present sufficient conditions for asymptotic stability and exponential stability of a class of impulsive neutral differential equations with discrete and distributed delays. Our approaches are based on the method using…
This paper provides new summation inequalities in both single and double forms to be used in stability analysis of discrete-time systems with time-varying delays. The potential capability of the newly derived inequalities is demonstrated by…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…
This paper explores the exponential stability of two nonlinear wave equations coupled through their velocities. The analysis is divided into two main cases. First, we consider a system where one equation is damped, while the other…
An equilibrium of a delay differential equation (DDE) is absolutely stable, if it is locally asymptotically stable for all delays. We present criteria for absolute stability of DDEs with discrete time-delays. In the case of a single delay,…
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system,…
In this paper, we introduce the notion of boundary delay equations, establishing a unified framework for analyzing linear time-invariant systems with pure time-delayed boundary conditions. We establish mild sufficient conditions for the…
This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of…
A nonlinear cyclic system with delay and the overall negative feedback is considered. The characteristic equation of the linearized system is studied in detail. Sufficient conditions for the oscillation of all solutions and for the…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
This paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the…
Robust hyperbolicity and stability results for linear partial differential equations with delay will be given and, as an application, the effect of small delays to the asymptotic properties of feedback systems will be analyzed.
Hyperexponential stability is investigated for dynamical systems with the use of both, explicit and implicit, Lyapunov function methods. A nonlinear hyperexponential control is designed for stabilizing linear systems. The tuning procedure…
We study the stability properties of linear time-varying systems in continuous time whose system matrix is Metzler with zero row sums. This class of systems arises naturally in the context of distributed decision problems, coordination and…
For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…
This paper deals with the stability analysis of a nonlinear time-delayed dispersive equation of order four. First, we prove the well-posedness of the system and give some regularity results. Then, we show that the zero solution of the…