This article is cited in 3 papers

Research articles

Asymptotic Stability of autonomous and Non-Autonomous Discrete Linear Inclusions

D. Cheban^a, C. Mammana<sup>b

a</sup> Moldova State University, Department of Mathematics and Informatics, Chişinău, Moldova
^b Institute of Economics and Finances, University of Macerata, Macerata, Italy

Abstract: The article is devoted to the study of absolute asymptotic stability of discrete linear inclusions (both autonomous and non-autonomous) in Banach space. We establish the relation between absolute asymptotic stability, uniform asymptotic stability and uniform exponential stability. It is proved that for compact (completely continuous) discrete linear inclusions these notions of stability are equivalent. We study this problem in the framework of non-autonomous dynamical systems (cocyles).

Keywords and phrases: Absolute asymptotic stability, cocycles, set-valued dynamical systems, global attractors, uniform exponential stability, discrete linear inclusions.

MSC: Primary 34C35, 34D20, 34D40, 34D45, 58F10, 58F12, 58F39; Secondary 35B35, 35B40

Received: 12.12.2004

Language: English

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