The small μ theorem without real-rational assumption

The classical statement of the small μ theorem requires that the plant P(s) (resp. P(z)) be real-rational. In the case of purely dynamic uncertainty, obvious extensions to the general case easily follow from subharmonicity of the “complex μ”. In this paper we point out that, with real or mixed uncertainty, some care must be exercised in stating such extensions, at least if P(s) (resp. P(z)) is allowed to take on non-real values on the real axis. We state and prove a small μ theorem that holds in the general case