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In this paper, we provide a necessary and sufficient condition ensuring the property of exponential dichotomy for periodic linear systems of generalized differential equations. This condition allow us to revisit a recent result of…
In the paper https://doi.org/10.1016/j.physleta.2011.08.072 authors propose a modification of the conventional delayed feedback control algorithm, where time-delay is varied continuously to minimize the power of control force. Minimization…
This paper presents new sufficient conditions for convergence and asymptotic or exponential stability of a stochastic discrete-time system, under which the constructed Lyapunov function always decreases in expectation along the system's…
By developing new efficient techniques and using an appropriate fixed point theorem, we derive several new sufficient conditions for the pseudo almost periodic solutions with double measure for some system of differential equations with…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
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…
We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and…
Under a precise nonlinearity-diffusivity condition we establish the decay of space-periodic entropy solutions of a multidimensional degenerate nonlinear parabolic equation.
We consider the problem of pointwise stabilization of a one-dimensional wave equation with an internal spatially varying anti-damping term. We design a feedback law based on the backstepping method and prove exponential stability of the…
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…
We give a sufficient condition for exponential stability of a network of lossless telegrapher's equations, coupled by linear time-varying boundary conditions. The sufficient conditions is in terms of dissipativity of the couplings, which is…
For ordinary differential equations and functional differential equations the following result is well known. Suppose any solution is bounded on the half-line for each bounded on the half-line right-hand side. Then under certain conditions…
Distributed delay equations have been used to model situations in which there is some sort of delay whose duration is uncertain. However, the interpretation of a distributed delay equation is actually very different from that of a delay…
We study an axial dispersion tubular reactor model governed by a nonlinear parabolic equation with Robin-type boundary conditions and boundary feedback control. We derive sufficient conditions for the exponential stability of the…
For a sample of Exponentially distributed durations we aim at point estimation and a confidence interval for its parameter. A duration is only observed if it has ended within a certain time interval, determined by a Uniform distribution.…
The decay of a quasiparticle in an isolated quantum dot is considered. At relatively small time the probability to find the system in the initial state decays exponentially: $P(t)\sim \exp(-\Gamma t)$, in accordance with the golden rule.…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
A modified method of functional constraints is used to construct the exact solutions of nonlinear equations of reaction-diffusion type with delay and which are associated with variable coefficients. This study considers a most generalized…
A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best…
Near-deterministic positive delays require highly concentrated distributions, but phase-type models are constrained by the Erlang variance limit. While matrix-exponential distributions can empirically bypass this barrier, prior low-variance…