A characterisation of common diagonal stability over cones

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 .