This study is concerned with the problem of adaptive sliding mode control (SMC) for uncertain stochastic singular systems. A novel integral-type sliding surface function is first introduced based on a particular observer design, which incorporates both the state estimations and the outputs to achieve prescribed specifications. The analysis of mean-square asymptotic admissibility of the underlying sliding mode dynamics with $H ∞$ disturbance attenuation level for the closed-loop systems is performed to exploit a new condition via linear matrix inequality technique. Then, the reachability of the predesigned sliding surface is ensured within finite-time almost surely by utilising a novel adaptive SMC law. Two examples are provided to demonstrate the validity and potential of the proposed method.

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Observer-based adaptive $H ∞$ control of uncertain stochastic singular systems via integral sliding mode technique

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