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A method is described for the design of optimal linear servomechanisms. The system to be controlled is assumed to be linear, time invariant and multivariable. The cost function to be minimised is quadratic and is measured over an infinite time interval. Expressions are given to enable the optimal controllers for both open-loop and closed-loop systems to be calculated. A result is obtained that allows the cost function weighting terms to be related to the optimal-compensated system pole positions, and hence to the system transient response. The relationship can be used when choosing the weighting constants. The design procedure is illustrated in the design of a controller for a strip processing line for which the tension in the strip and the speed of the drives is to be controlled. A new method of spectral factorisation is also introduced. This can only be used on a restricted-class matrices having a degree of symmetry; however, it is much easier to use than previous methods.