SIAM Journal on Control and Optimization, Vol.52, No.3, 1809-1831, 2014
STABILITY ANALYSIS OF POSITIVE SEMI-MARKOVIAN JUMP LINEAR SYSTEMS WITH STATE RESETS
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.