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An adaptive inferential algorithm is developed for estimation and control of multirate systems. The output y is measured J times slower than the secondary process output v and the input u, but an output estimate ye is produced at each sampling interval of v and u. Compared with previous work on multirate inferential systems, the proposed algorithm has a more formal theoretical basis. For example, the output y is related to the secondary output v not only through external stochastic disturbances but also through the internal system structure. Convergence properties are formally proven for the case of zero external stochastic disturbances, and a simplified algorithm is proposed for practical applications. Simulated results illustrate the convergence properties of the algorithm and the improvement obtained in simple feedback control systems. The algorithm has direct application in the process industries.