Observations on robust diffusive stability and common Lyapunov functions

We consider the problem of robust diffusive stability (RDS) for a pair of coupled stable discrete-time positive linear-time invariant (LTI) systems. We first show that the existence of a common diagonal Lyapunov function is sufficient for RDS and highlight how this condition differs from recent results using linear copositive Lyapunov functions. We also present an extension of these results, showing that the weaker condition of \emph{joint} linear copositive function existence is also sufficient for RDS. Finally, we present two results on RDS for extended Leslie matrices arising in population dynamics.