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Gain and phase margin are two very common and important control design parameters. The amount of gain and phase margin that a system possesses is used to determine relative stability properties as well as other performance characteristics. They are several well developed techniques for designing systems with margin constraints. This problem becomes increasingly more difficult when the plant considered involves uncertainty. This paper shows that gain margin, phase margin, asymptotic tracking and asymptotic noise attenuation constraints can be posed as a robust polynomial stabilization requirement. We can apply the Finite Inclusions Theorem to develop algorithms for robust controller design that meet stability and performance requirements.