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We provide convex necessary and sufficient conditions for the robuststability of linear positively dominated systems. In particular we show thatthe structured singular value is always equal to its convex upper bound fornonnegative matrices and we use this result to derive necessary and sufficientLinear Matrix Inequality (LMI) conditions for robust stability that involveonly the system's static gain. We show how this approach can be applied to testthe robust stability of the Foschini-Miljanic algorithm for power control inwireless networks in presence of uncertain interference.

A Convex Characterization of Robust Stability for Positive and Positively Dominated Linear Systems