Robust stability and control of hybrid stochastic systems with time-delay

The paper considers a class of hybrid control systems described by the family of finite set of individual stochastic differential equations with time-delay. The discontinuous (jumping) transitions between the individual systems is described by the homogeneous Markov chain. The conditions of robust stability in the sense that the hybrid system is stochastically stable for arbitrary time-delay and arbitrary transition probabilities are obtained in both linear case and in the presence of Lur´e-type nonlinearities. The state feedback control law, which guarantees the robust stability of the closed-loop hybrid system in linear case is also given.