Stochastic stability of Ito differential equations with semi-Markovian jump parameters

In this note, the problem of stochastic stability for linear systems with jump parameters being semi-Markovian rather than full Markovian is further investigated. In particular, the system under consideration is described by Ito type nonlinear stochastic differential equations with phase type semi-Markovian jump parameters. Stochastic stability conditions are presented.