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This work deals with a scalar nonlinear neutral delay differential equation issued from the study of wave propagation. A critical value of the coefficients is considered, where only few results are known. The difficulty follows from 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…
Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This…
The ever increasing complexity of real-time control systems results in significant deviations in the timing of sensing and actuation, which may lead to degraded performance or even instability. In this paper we present a method to analyze…
The stabilization of uncertain LTI/LPV time delay systems with time varying delays by state-feedback controllers is addressed. At the difference of other works in the literature, the proposed approach allows for the synthesis of resilient…
Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…
This paper deals with the exponential stabilization of a time-delay system with an average of the state as the output. A general stability theorem with a guaranteed exponential decay-rate based on a Wirtinger-based inequality is provided.…
We present an analysis of time-delayed feedback control used to stabilize an unstable steady state of a neutral delay differential equation. Stability of the controlled system is addressed by studying the eigenvalue spectrum of a…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
We study the synchronization and stability of power grids within the Kuramoto phase oscillator model with inertia with a bimodal frequency distribution representing the generators and the loads. We identify critical nodes through solitary…
We study the stability of the fixed-point solution of an array of mutually coupled logistic maps, focusing on the influence of the delay times, $\tau_{ij}$, of the interaction between the $i$th and $j$th maps. Two of us recently reported…
The field of network synchronization has seen tremendous growth following the introduction of the master stability function (MSF) formalism, which enables the efficient stability analysis of synchronization in large oscillator networks.…
We consider a network of identical piecewise smooth systems that synchronizes on the manifold given by a periodic orbit of a single agent. We explicitly characterize the fundamental matrix solution of the network along the synchronous…
Absolute stability of discrete-time teleoperation systems can be jeopardized by choosing inappropriate sampling time architecture. A modified structure is presented for the bilateral teleoperation system including continuous-time slave…
This study examines the complex interplay between inertia and time delay in regular rotor networks within the framework of the second-order Kuramoto model. By combining analytical and numerical methods, we demonstrate that intrinsic time…
For networked systems, the control law is typically subject to network flaws such as delays and packet dropouts. Hence, the time in between updates of the control law varies unexpectedly. Here, we present a stability theorem for nonlinear…
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…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
In the study of dynamical systems on networks/graphs, a key theme is how the network topology influences stability for steady states or synchronized states. Ideally, one would like to derive conditions for stability or instability that…
We present a systematic approach to reveal the correspondence between time delay dynamics and networks of coupled oscillators. After early demonstrations of the usefulness of spatio-temporal representations of time-delay system dynamics,…