ℓ∞-stability analysis of discrete autonomous systems described by Laurent polynomial matrix operators

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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