Disturbance-Observer-Based Composite Hierarchical Antidisturbance Control for Singular Markovian Jump Systems

Antidisturbance control issue for singular Markovian jump systems under infinitely unobservable states and multiple disturbances is investigated. One of the disturbances is norm bounded, whereas the other is written in a state-space expression. Under assumption that some of the states of the system are infinitely unobservable, a novel mode-dependent observer is proposed to estimate the modeling disturbance and all the states by equivalent transforming and reformulating the system into a reduced-order system where the observable states are included and infinitely unobservable states are regarded as an unknown input. Then, we construct a composite hierarchical controller based on the outputs of the proposed observer. Sufficient conditions for the existence of the desired observer gains and controller matrices are derived. Finally, a simulation example is presented to demonstrate the effectiveness of our scheme.