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At first, the study establishes an asynchronous observer and correspondingly constructs a sliding mode switching function in which the controller gain operates asynchronously with the original system. Then the observer-based SMC law is designed through Lyapunov stability theory to achieve reachability of the specified sliding surface, resulting in mean-square stability of the closed-loop system. In addition, we extend the aforementioned findings to a more practical case where the conditional probability is only partially known. 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