The problems of stochastic stability and stochastic disturbance attenuation for a class of linear discretetime
systems are considered in this paper. The system under study is a state space model possessing two Markovian jump parameters: one is failure process and another is failure detection and isolation scheme. A controller is designed to guarantee the stochastic stability and a disturbance attenuation level. Robustness problems for the above system with norm-bounded parameter uncertainties are also investigated. It is shown that the uncertain system can be robustly stochastically stabilized and have a robust disturbance attenuation level for all admissible perturbations if a set of coupled Riccati inequalities has solutions. A numerical example is given to show the potential of the proposed technique. Copyright