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We consider a nonlinear evolution problem with an asymptotic parameter and construct examples in which the linearized operator has spectrum uniformly bounded away from Re z >= 0 (that is, the problem is spectrally stable), yet the nonlinear…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…
We prove a new linearization principle for the nonlinear stability of solutions to semilinear evolution equations of parabolic type. We assume that the set of equilibria forms a finite dimensional manifold of normally stable and normally…
We consider several classes of degenerate hyperbolic equations involving delay terms and suitable nonlinearities. The idea is to rewrite the problems in an abstract way and, using semigroup theory and energy method, we study well posedness…
In this paper, we discuss the existence and asymptotic stability of the positive periodic mild solutions for the abstract evolution equation with delay in an ordered Banach space $E$, $$u'(t)+Au(t)=F(t,u(t),u(t-\tau)),\ \ \ \ t\in\R,$$…
There are several results on the stability of nonlinear positive systems in the presence of time delays. However, most of them assume that the delays are constant. This paper considers time-varying, possibly unbounded, delays and…
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…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…
In this paper, we investigate the global exponential stability for complex-valued recurrent neural networks with asynchronous time delays by decomposing complex-valued networks to real and imaginary parts and construct an equivalent…
We prove the equivalence of the well-posedness of a partial differential equation with delay and an associated abstract Cauchy problem. This is used to derive sufficient conditions for well-posedness, exponential stability and norm…
The paper emphasizes the property of stability for skew-evolution semiflows on Banach spaces, defined by means of evolution semiflows and evolution cocycles and which generalize the concept introduced by us in a previous paper. There are…
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…
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 discusses the in-domain feedback stabilization of reaction-diffusion PDEs with Robin boundary conditions in the presence of an uncertain time- and spatially-varying delay in the distributed actuation. The proposed control design…
For vibrating systems, a delay in the application of a feedback control can destroy the stabilizing effect of the control. In this paper we consider a vibrating string that is fixed at one end and stabilized with a boundary feedback with…
We prove the well-posedness of a linear closed-loop system with an explicit (already known) feedback leading to arbitrarily large decay rates. We define a mild solution of the closed-loop problem using a dual equation and we prove that the…
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…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…
We study the asymptotics of strongly continuous operator semigroups defined on locally convex spaces in order to develop a stability theory for solutions of evolution equations beyond Banach spaces. In the classical case, there is only…