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A new method is presented for the design of simply structured multivariable controllers that can explicitly meet mixed sensitivity robust performance and robust stability criteria. Currently, most established robust controller design methods are synthesis-based and produce controllers that are often of much higher order than the plant. Based on the technique of diagonal dominance, this method proposes a novel means of directly 'designing' a robust controller, which among others, has the benefit that its order can be determined by the designer. By using elementary algebra, it is shown that the Gershgorin disks of a matrix may also be used to bind its singular values in addition to the eigenvalues. This fact is then exploited to create simple envelopes that bind the singular values of the sensitivity and complementary sensitivity functions, which are subsequently used in the design of the diagonal dominance-based controller such that the mixed criteria on the loop transfer function sensitivities may be met. As with other mixed sensitivity design techniques, this method does not guarantee that a controller is feasible for any set of arbitrary specifications. The method is applied to design a mixed-sensitivity controller for a mathematical model of the Rolls-Royce gas-turbine engine.