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The use of the linear quadratic optimal problem (LQ) and the linear quadratic Gaussian (LQG) methodologies for the design of multivariable control systems is reviewed. The past decade has seen further developments in the solution procedures for these problems; in particular, the frequency domain techniques have experienced considerable refinement. The practical problems arising from the LQ/LQG methodology have also been the subject of considerable theoretical analysis. In the sequel, the recent frequency domain ideas are presented including the use of generalised spectral factor and polynomial systems theory. The practical aspects which are reviewed include the selection of performance criterion weighting matrices, robustness and integrity. Looking to the future, the newer research areas of optimal robustness and the application of LQG controllers in self-tuning control systems are also discussed.