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Integral Characterizations for Uniform Stability with Growth Rates in Banach Spaces

Axioms, 2021
The aim of this paper is to present some integral characterizations for the concept of uniform stability with growth rates in Banach spaces. In this sense, we prove necessary and sufficient conditions (of Barbashin and Datko type) for an evolution ...
Rovana Boruga (Toma), Mihail Megan, Daniela Maria-Magdalena Toth   +2 more
doaj   +3 more sources

On the uniform exponential stability of linear time-delay systems [PDF]

International Journal of Mathematics and Mathematical Sciences, 2004
This paper deals with the global uniform exponential stability independent of delay of time-delay linear and time-invariant systems subject to point and distributed delays for the initial conditions being continuous real functions except possibly on a ...
M. de la Sen, Ningsu Luo
doaj   +6 more sources

On the uniform exponential stability of linear skew-product semiflows [PDF]

Journal of Function Spaces and Applications, 2006
The problem of uniform exponential stability of linear skew-product semiflows on locally compact metric space with Banach fibers, is discussed. It is established a connection between the uniform exponential stability of linear skewproduct semiflows and ...
Ciprian Preda
doaj   +2 more sources

On Uniform Exponential Stability and Exact Admissibility of Discrete Semigroups [PDF]

International Journal of Differential Equations, 2013
We prove that a discrete semigroup 𝕋={T(n):n∈ℤ+} of bounded linear operators acting on a complex Banach space X is uniformly exponentially stable if and only if, for each x∈AP0(ℤ+,X), the sequence n↦∑k=0n‍T(n-k)x(k):ℤ+→X belongs to AP0(ℤ+,X).
Aftab Khan, Gul Rahmat, Akbar Zada
doaj   +3 more sources

On relation between uniform asymptotic stability and exponential stability of linear differential equations

Electronic Journal of Qualitative Theory of Differential Equations, 2015
We present such a restriction on parameters of linear functional differential equations of retarded type that is sufficient for the uniform asymptotic stability of an equation to be equivalent to its exponential stability.
Andrew Kulikov, Vera Malygina
doaj   +2 more sources

Uniform exponential stability of linear almost periodic systems in Banach spaces

Electronic Journal of Differential Equations, 2000
This article is devoted to the study linear non-autonomous dynamical systems possessing the property of uniform exponential stability. We prove that if the Cauchy operator of these systems possesses a certain compactness property, then the uniform ...
David N. Cheban
doaj   +4 more sources

Uniform exponential stability of linear periodic systems in a Banach space

Electronic Journal of Differential Equations, 2001
This article is devoted to the study of linear periodic dynamical systems, possessing the property of uniform exponential stability. It is proved that if the Cauchy operator of these systems possesses a certain compactness property, then the asymptotic ...
David N. Cheban
doaj   +2 more sources

Practical Semiglobal Uniform Exponential Stability Of Nonlinear Nonautonomous Systems

Ukrainian Mathematical Journal, 2023
UDC 517.9 We solve the following twofold problem: In the first part, we deduce Lyapunov sufficient conditions for practical uniform exponential stability of nonlinear perturbed systems under  different conditions for the perturbed term. The second part presents a converse Lyapunov theorem for the notion of semiglobal uniform exponential stability ...
Kicha, A., Hammami, M. A., Abbes, I.-E.
openaire   +2 more sources

Lyapunov Characterization of Uniform Exponential Stability for Nonlinear Infinite-Dimensional Systems [PDF]

IEEE Transactions on Automatic Control, 2022
In this paper we deal with infinite-dimensional nonlinear forward complete dynamical systems which are subject to external disturbances. We first extend the well-known Datko lemma to the framework of the considered class of systems. Thanks to this generalization, we provide characterizations of the uniform (with respect to disturbances) local, semi ...
Haidar, Ihab, Chitour, Yacine, Mason, Paolo, Sigalotti, Mario   +3 more
openaire   +3 more sources

On Uniform Stability with Growth Rates of Stochastic Skew-Evolution Semiflows in Banach Spaces

Axioms, 2021
The main purpose of this paper is to study a more general concept of uniform stability in mean in which the uniform behavior in the classical sense is replaced by a weaker requirement with respect to some probability measure.
Tímea Melinda Személy Fülöp, Mihail Megan, Diana Ioana Borlea(Pătraşcu)   +2 more
doaj   +1 more source