A more practical formulation for robustness analysis

The structured singular value mu has proved its usefulness in assessing the stability of a linear time-invariant model submitted to structured perturbations (real parametric perturbations or model perturbations). For this purpose, the model must be cast in a special form: a linear time-invariant system connected with a block-diagonal uncertainty operator whose gain is less than one. For practical purposes, such a formulation is nevertheless awkward when considering some problems of interest, such as one-sided stability analysis or distance to passivity. We propose a new, more general and flexible formulation, which allows one to address these problems in a direct way. This extension relies on the sector notion developed by M.G. Safonov (1980). For the computation of the margin associated with our formulation, we propose an extension of the upper bound of mu.Anglai