Related papers: Stability of solutions to nonlinear wave equations…
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…
The goal of the present paper is to study the viscoelastic wave equation with the time delay \[ |u_t|^\rho u_{tt}-\Delta u-\Delta u_{tt}+\int_0^tg(t-s)\Delta u(s)ds+\mu_1u_t(x,t)+\mu_2 u_t(x,t-\tau)=b|u|^{p-2}u\] under initial boundary…
This paper gives necessary and sufficient conditions for the convergence of the solution of a weakly damped second order linear differential equation that is subjected to outside forcing, for which solutions of the unforced equation are…
We study the question of existence of positive steady states of nonlinear evolution equations. We recast the steady state equation in the form of eigenvalue problems for a parametrised family of unbounded linear operators, which are…
We consider an abstract second order evolution equation with damping. The "elastic" term is represented by a self-adjoint nonnegative operator A with discrete spectrum, and the nonlinear term has order greater than one at the origin. We…
This work establishes the first rigorous stability guarantees for approximate predictors in delay-adaptive control of nonlinear systems, addressing a key challenge in practical implementations where exact predictors are unavailable. We…
Discrete-time systems under aperiodic sampling may serve as a modeling abstraction for a multitude of problems arising in cyber-physical and networked control systems. Recently, model- and data-based stability conditions for such systems…
We consider a class of nonlinear Schr\"odinger equation in two space dimensions with an attractive potential. The nonlinearity is local but rather general encompassing for the first time both subcritical and supercritical (in $L^2$)…
This paper addresses the problem of stabilization for infinite-dimensional systems. In particular, we design nonlinear stabilizers for both linear and nonlinear abstract systems. We focus on two classes of systems: the first class comprises…
We study asymptotic behavior of solutions of the first-order linear consensus model with delay and anticipation, which is a system of neutral delay differential equations. We consider both the transmission-type and reaction-type delay that…
Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…
This paper addresses the stabilization of linear systems with multiple time-varying input delays. In scenarios where neither the exact delays information nor their bound is known, we propose a class of linear time-varying state feedback…
In this paper we consider an interior stabilization problem for the wave equation with dynamic boundary delay.We prove some stability results under the choice of damping operator. The proof of the main result is based on a frequency domain…
We establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…
The purpose of this paper is to investigate the stabilization of a one-dimensional coupled wave equations with non smooth localized viscoelastic damping of Kelvin-Voigt type and localized time delay. Using a general criteria of…
In this paper we consider a stabilization problem for the abstract-wave equation with delay. We prove an exponential stability result for appropriate damping coefficient. The proof of the main result is based on a frequency-domain approach.
In this paper we characterize the output feedback stabilization of some coupled systems with delay. The proof of the main result uses the method introduced in Ammari and Tucsnak \cite{at} where the exponential stability for the closed loop…
The stability analysis of a class of discontinuous discrete-time systems is studied in this paper. The system under study is modeled as a feedback interconnection of a linear system and a set-valued nonlinearity. An equivalent…
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…
In this paper, we establish nonlinear Landau damping and asymptotic stability of a large class of translation-invariant steady solutions to the time-dependent Hartree--Fock equations in the presence of an {\em off-diagonal exchange…