The small /spl mu/ theorem without real-rational assumption

摘要

The classical statement of the small /spl mu/ 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 /spl mu/". 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 /spl mu/ theorem that holds in the general case.