Abstract
We prove small-gain type criteria of exponential stability for positive linear discrete-time systems in ordered Banach spaces that have a normal and generating positive cone. Such criteria play an important role in the finite-dimensional systems theory but are rather unexplored in the infinite-dimensional setting, yet. Furthermore, we show that our stability criteria can be considerably strengthened if the cone has non-empty interior or if the operator inducing the discrete-time system is quasi-compact.
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