Fault-Tolerant Control of Time-Delay Markov Jump Systems With <inline-formula> <tex-math notation="LaTeX"> $It\hat{o}$</tex-math> </inline-formula> Stochastic Process and Output Disturbance Based on Sliding Mode Observer

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This paper focuses on the fault-tolerant control problem of Markov jump systems (MJS) with $It\hat{o}$ stochastic process and output disturbances. Such a problem widely exists in practical systems such as mobile manipulator systems. Since MJS can suitably describe mobile manipulator systems, in this paper, a new approach based on the MJS model is proposed. First, a proportional-derivative sliding mode observer (SMO) and an observer-based controller are designed and synthesized. Two new theorems are derived to ensure the close-loop stochastic stability and the reachability of the sliding mode surface. Compared with the existing works, the system model is more general, which could describe a larger variety of plants or processes. The controller design procedure is simplified by solving the sliding mode parameters and the controller gain simultaneously with only one linear matrix inequality problem. In addition, the augmented fault vector can be reconstructed by employing a descriptor SMO. Simulations are provided to demonstrate the validity of the derived theorems and the effectiveness of the proposed algorithm.