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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.
Yao et al. (Wed,) studied this question.