Mean stability of continuous-time semi-Markov jump linear positive systems

In this paper we study the mean stability of continuous-time semi-Markov jump linear positive systems, which are switched linear systems such that their state variables are in positive orthants and their switching signal is a Markov renewal process. The main result of this paper shows that the mean stability is determined by the spectral radius of a matrix. In the proof we utilize a stability-preserving discretization of continuous-time semi-Markov jump linear systems. The obtained results are demonstrated through the stability analysis and the stabilization of linear time-invariant systems with controller failures.