Stochastic stability of a class of nonlinear systems with randomly varying time-delay

This article studies the mean square stochastic stability of a class of continuous time nonlinear systems with a time-varying, random delay. The criteria for stability of systems of this kind are important for industrial embedded control applications. The evolution of the delay is modelled by a continuous-time Markov process with a finite number of states. The global asymptotic mean-square stochastic stability conditions are given in terms of transition probabilities of the Markov process and stability properties of the system with a constant delay