Regularity conditions for robust stability problems with linearly structured perturbations

The problem of continuity of the stability margin of a control system on problem input data is addressed. The case in which perturbations are linearly correlated is considered. It is shown that the existence of special points (called critical points) of the stability boundary manifold in parameter space plays a key role in the analysis of the problem. Several conditions, either only sufficient or necessary and sufficient, are given ensuring continuity of the stability margin on problem data. These conditions show that possible discontinuity phenomena may happen only in very exceptional (nongeneric) cases