Numerical Algorithms

, Volume 58, Issue 4, pp 529–543 | Cite as

Stability verification for monotone systems using homotopy algorithms

  • Björn S. RüfferEmail author
  • Fabian R. Wirth
Original Paper


A monotone self-mapping of the nonnegative orthant induces a monotone discrete-time dynamical system which evolves on the same orthant. If with respect to this system the origin is attractive then there must exist points whose image under the monotone map is strictly smaller than the original point, in the component-wise partial ordering. Here it is shown how such points can be found numerically, leading to a recipe to compute order intervals that are contained in the region of attraction and where the monotone map acts essentially as a contraction. An important application is the numerical verification of so-called generalized small-gain conditions that appear in the stability theory of large-scale systems.


Monotone systems Stability theory Homotopy algorithms 

Mathematics Subject Classifications (2010)

93C55 47H07 65H20 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Institut für Elektrotechnik und InformationstechnikUniversität PaderbornPaderbornGermany
  2. 2.Institut für MathematikUniversität WürzburgWürzburgGermany

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