  This paper studies the mean stability of positive semi-Markovian jump linear
systems. We show that their mean stability is characterized by the spectral
radius of a matrix that is easy to compute. In deriving the condition we use a
certain discretization of a semi-Markovian jump linear system that preserves
stability. Also we show a characterization for the exponential mean stability
of continuous-time positive Markovian jump linear systems. Numerical examples
are given to illustrate the results.
