New Aspects of Nonautonomous Discrete Systems Stability

Authors

Dhaou Lassoued, Laboratoire SAMM EA4543, Universit´e Paris 1 Panth´eon-Sorbonne, centre P.M.F., 90 rue de Tolbiac 75634 Paris cedex 13, FranceFollow

Author Country (or Countries)

France

Abstract

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.

Recommended Citation

Lassoued, Dhaou (2015) "New Aspects of Nonautonomous Discrete Systems Stability," Applied Mathematics & Information Sciences: Vol. 09: Iss. 4, Article 5.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss4/5