17th International Symposium on
Mathematical Theory of Networks and Systems
Kyoto International Conference Hall, Kyoto, Japan, July 24-28, 2006

MTNS 2006 Paper Abstract

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Paper MoA09.3

Rüffer, Björn S. (Univ. Bremen), Wirth, Fabian R. (National Univ. of Ireland at Maynooth), Dashkovskiy, Sergey N. (Univ. of Bremen)

Discrete time monotone systems: Criteria for global asymptotic stability and applications

Scheduled for presentation during the Regular Session "Large Scale Systems" (MoA09), Monday, July 24, 2006, 11:40−12:05, Room J

17th International Symposium on Mathematical Theory of Networks and Systems, July 24-28, 2006, Kyoto, Japan

This information is tentative and subject to change. Compiled on March 29, 2024

Keywords Stability analyisis, Large scale systems, Systems on graphs

Abstract

For two classes of monotone maps on the n-dimensional positive orthant we show that for a discrete dynamical system induced by a map the origin of $R^n$ is globally asymptotically stable, if and only if the map is such that for any point in s in Rn, s>=0 but not zero, the image-vector is such that at least one component is strictly less than the corresponding component of s. One class is the set of n x n matrices of class K functions; these induce monotone operators on Rn. Maps of the other class satisfy some geometric property for an invariant set.