Revisiting stability of positive linear discrete-time systems

Titelangaben

Glück, Jochen ; Mironchenko, Andrii:
Revisiting stability of positive linear discrete-time systems.
In: IFAC-PapersOnLine. Bd. 55 (2022) Heft 30 . - S. 37-42.
ISSN 2405-8963
DOI: https://doi.org/10.1016/j.ifacol.2022.11.025

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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.