  In this study, we investigate the robust feedback stability problem for
multiple-input-multiple-output linear time-invariant systems involving
sectored-disk uncertainty, namely, dynamic uncertainty subject to simultaneous
gain and phase constraints. This problem is thereby called a sectored-disk
problem. Employing a frequency-wise analysis approach, we derive a fundamental
static matrix problem that serves as a key component in addressing the feedback
stability. The study of this matrix problem heavily relies on the
Davis-Wielandt (DW) shells of matrices, providing a profound insight into
matrices subjected to simultaneous gain and phase constraints. This
understanding is pivotal for establishing a less conservative sufficient
condition for the matrix sectored-disk problem, from which we formulate several
robust feedback stability conditions against sectored-disk uncertainty.
Finally, several conditions based on linear matrix inequalities are developed
for efficient computation and verification of feedback robust stability against
sectored-disk uncertainty.
