Convex characterization of robust stability analysis and control synthesis for positive linear systems

We present necessary and sufficient conditions for robust stability of positive systems. In particular we show that for such systems the structured singular value is equal to its convex upper bound and thus it can be computed efficiently. Using this property, we show that the problem of finding a structured static state feedback controller achieving internal stability, contractiveness, and internal positivity in closed loop remains convex and tractable even in the presence of uncertainty.