A. Mironchenko. Revisiting stability of positive linear discrete time systems.
Speaker:
Andrii Mironchenko (University of Passau)
http://www.mironchenko.com/
Title:
Revisiting stability of positive linear discrete-time systems
Slides:
http://mironchenko.com/__My_php_sourc...
Talk at 25th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2022)
Journal Paper (Open Access):
J. Glück, A. Mironchenko. Stability criteria for positive linear discrete-time systems. Positivity, 25(5):2029–2059, 2021.
https://link.springer.com/article/10....
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.
In the journal paper (but not in the talk), to place our results into context, we include an overview of known stability criteria for linear (and not necessarily positive) operators and provide full proofs for several folklore characterizations from this domain.
Date:
Monday, 12 September 2022