Related papers: Stabilizing effect of delay in higher dimensions
We investigate stability of linear delay differential systems. Stability criteria of the systems are derived based on integrals of the fundamental matrix. They are necessary and sufficient conditions for delay-dependent stability of the…
Time delays may cause dramatic changes to the dynamics of interacting oscillators. Coupled networks of interacting dynamical systems can behave unexpectedly when the signal between the vertices are time delayed. It has been shown for a very…
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…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
We study the effect of a time-delayed feedback within a generic model for a saddle-node bifurcation on a limit cycle. Without delay the only attractor below this global bifurcation is a stable node. Delay renders the phase space…
We reinvestigate the dynamical behavior of a first order scalar nonlinear delay differential equation with piecewise linearity and identify several interesting features in the nature of bifurcations and chaos associated with it as a…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
This paper presents the analysis of the stability properties of PID controllers for dynamical systems with multiple state delays, focusing on the mathematical characterization of the potential sensitivity of stability with respect to…
We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.
This paper concerns some spectral properties of the scalar dynamical system defined by a linear delay-differential equation with two positive delays. More precisely, the existing links between the delays and the maximal multiplicity of the…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
This paper is concerned with the problem of robust stabilization for a class of uncertain 2D discrete switched systems with state delays represented by a model of Roesser type, where the switching instants of the controller experience…
This work proposes a new procedure for the stabilization of time-delay systems using Static Output Feedback (SOF) control. A previous convex optimization approach to SOF for Ordinary Differential Equations (ODEs) is extended to time-delay…
Self-regulatory models are common in nature, as described e.g. in (\cite{mur}), (\cite{ha}) and (\cite{Gb}).\\ Let us consider a system made up of a number of glands as a motivation. Each gland secretes a hormone that allows secretion in…
Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When…
Although the theory of density evolution in maps and ordinary differential equations is well developed, the situation is far from satisfactory in continuous time systems with delay. This paper reviews some of the work that has been done…
Consider the question of building a system of commands remotely controlled robot that can perform motion stabilization in the presence of a constant delay of the control signal.
We consider a class of scalar delay differential equations with impulses and satisfying an Yorke-type condition, for which some criteria for the global stability of the zero solution are established. Here, the usual requirements about the…
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…