Interval observer-based fault-tolerant control for a class of positive Markov jump systems

The problem of fault-tolerant controller design for positive Markov jump systems subject to interval uncertainties and time-varying actuator faults is investigated in this paper. First, under the assumption of stochastic stability, an interval observer is developed to achieve simultaneously estimation of the upper and lower bounds of the system state and the actuator faults. Then, an interval observer and a state-estimate stabilizing feedback controller are jointly designed. By utilizing the obtained interval estimates, the controller is constructed to achieve a satisfactory performance and fault tolerance. Owing to positivity, the joint observer and controller design is formulated in terms of linear programming. The effectiveness of the proposed approach is demonstrated through simulation.