Adaptive decoupling is an important practical problem in industrial control. The idea is to compensate, adaptively, for interactions in multivariable control and then complete the design with single-input single-output techniques.
In the paper a decoupling precompensator is first derived based on results by {\it C. A. Desoer} and {\it A. N. Gündes} [IEEE Trans. Avtom. Control AC-31, 744-750 (1986;

Zbl 0603.93029)], when the model is known. The prior knowledge needed for the design of the precompensator is the “delay structure” of the process. Computationally common factors of polynomials must be found at each step. For adaptive implementation, it is assumed that the shortest delay in each row of the control matrix is known. This means assuming that delay between each of the inputs and outputs is known. Parameters are updated by a recursive estimation scheme, which is slightly modified from the basic least squares estimation. Under some technical assumptions convergence of the adaptive decoupler is shown. This together with complete decoupling is the major contribution of the paper.