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For a generalised minimum variance controller algorithm the weighting polynomials are calculated in such a way as to assign the closed-loop poles of the system and to reduce the output and control signals variances. This technique is based on the fact that the pole-assignment equation may have multiple solutions if the weighting polynomials are not of minimal order. By increasing the order of these polynomials, degrees of freedom are obtained which are utilised to minimise a linear combination of the output and control signals variances. The result is an improvement of the stochastic behaviour without change in the deterministic behaviour of the system.