Abstract
In this paper, we analyze the ℓ∞-stability of infinite dimensional discrete autonomous systems, whose dynamics is governed by a Laurent polynomial matrix A(σ,σ−1) in shift operator σ on vector valued sequences. We give necessary and sufficient conditions for the ℓ∞-stability of such systems. We also give easy to check tests to conclude or to rule out the ℓ∞-stability of such systems.
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