On exponential dichotomy of variational difference equations.
On dichotomous behavior of variational difference equations and applications.
Stability of difference equations and applications to robustness problems.
Translation invariant spaces and asymptotic properties of variational equations.
Integral equations and exponential trichotomy of skew-product flows.
Stabilizability and controllability of systems associated to linear skew-product semiflows.
This paper is concerned with systems with control whose state evolution is described by linear skew-product semiflows. The connection between uniform exponential stability of a linear skew-product semiflow and the stabilizability of the associated system is presented. The relationship between the concepts of exact controllability and complete stabilizability of general control systems is studied. Some results due to Clark, Latushkin, Montgomery-Smith, Randolph, Megan, Zabczyk and Przyluski are generalized....
Exponential expansiveness and complete admissibility for evolution families
Connections between uniform exponential expansiveness and complete admissibility of the pair are studied. A discrete version for a theorem due to Van Minh, Räbiger and Schnaubelt is presented. Equivalent characterizations of Perron type for uniform exponential expansiveness of evolution families in terms of complete admissibility are given.
Banach function spaces and exponential instability of evolution families
In this paper we give necessary and sufficient conditions for uniform exponential instability of evolution families in Banach spaces, in terms of Banach function spaces. Versions of some well-known theorems due to Datko, Neerven, Rolewicz and Zabczyk, are obtained for the case of uniform exponential instability of evolution families.
Exponential stability and exponential instability for linear skew-product flows
We give characterizations for uniform exponential stability and uniform exponential instability of linear skew-product flows in terms of Banach sequence spaces and Banach function spaces, respectively. We present a unified approach for uniform exponential stability and uniform exponential instability of linear skew-product flows, extending some stability theorems due to Neerven, Datko, Zabczyk and Rolewicz.
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