Recently, it was shown that the structured singular value framework can be extended to the case when information on the phase of the uncertainty is available, and a computable upper bound on the corresponding "phase sensitive structured singular value" was obtained. Here we show that the same bound can be obtained via an entirely different approach, using a family of linear fractional transformations. Extension to various uncertainty "shapes" follows.
The "median phase" and "phase spread" of a matrix are defined and properties are derived. The question of robust stability under uncertainty with phase information is addressed and a corresponding necessary and sufficient condition is given. This condition involves a "phase sensitive singular value". A computable upper bound to this quantity is obtained. The case when the uncertainty is block-structured is also considered.
