Stability analysis of systems with stochastically varying delays

A stability analysis of linear systems with stochastically varying delay is performed. It is assumed that the delay function has the form of a sawtooth with switches occurring at the arrival times of a homogeneous Poisson process. Several notions of stochastic stability are considered and corresponding stability criteria are derived. For two examples the different criteria are compared and the effect on stability of various deterministic approximations is examined.