A characterisation of common diagonal stability over cones

Abstract

In this article, a general notion of common diagonal Lyapunov matrix is formulated for a collection of n × n matrices A ₁, … , A _s , and cones k ₁, … , k _s in ℝ ⁿ . Necessary and sufficient conditions are derived for the existence of a common diagonal Lyapunov matrix in this setting. The conditions are similar to and extend the well-known criteria for the case s = 1, k ₁ = ℝ ⁿ .

Keywords:

• stability over cones
• common diagonal Lyapunov matrix over cones
• co-positive matrices
• completely positive matrices

AMS Subject Classifications::

• 32Q26
• 34D20
• 19605
• 15B48
• 47L07

Acknowledgements

The third author is supported by SFI grant 07/IN.1/I901.