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SM ISO690:2012 CHEBAN, David, MAMMANA, Cristiana. Absolute Asymptotic Stability of Discrete Linear Inclusions. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2005, nr. 1(47), pp. 43-68. ISSN 1024-7696. |
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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
Numărul 1(47) / 2005 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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Pag. 43-68 | ||||||
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Rezumat | ||||||
The article is devoted to the study of absolute asymptotic stability
of discrete linear inclusions in Banach (both finite and infinite dimensional) space.
We establish the relation between absolute asymptotic stability, asymptotic stability,
uniform asymptotic stability and uniform exponential stability. It is proved that for
asymptotical compact (a sum of compact operator and contraction) discrete linear
inclusions the notions of asymptotic stability and uniform exponential stability are
equivalent. It is proved that finite-dimensional discrete linear inclusion, defined by
matrices {A1,A2, ...,Am}, is absolutely asymptotically stable if it does not admit
nontrivial bounded full trajectories and at least one of the matrices {A1,A2, ...,Am}
is asymptotically stable. We study this problem in the framework of non-autonomous
dynamical systems (cocyles). |
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