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New Aspects of Nonautonomous Discrete Systems Stability |
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PP: 1693-1698 |
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Author(s) |
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Dhaou Lassoued,
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Abstract |
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| We prove that a discrete evolution family U := {U(n,m) : n ≥ m ∈ Z+} of bounded linear operators acting on a complex
Banach space X is uniformly esponentially stable if and only if for each forcing term ( f (n))n∈Z+ belonging to AP0(Z+,X), the solution
of the discrete Cauchy Problem
x(n+1) = A(n)x(n)+ f (n), n ∈ Z+
x(0) = 0
belongs also to AP0(Z+,X), where the operators-valued sequence (A(n))n∈Z+ generates the evolution family U. The approach we use
is based on the theory of discrete evolution semigroups associated to this family. |
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