On Robust Stability of Linear State Space Models.

Abstract

The structured singular value (MU), introduced by Doyle [1] allows to analyze robust stability and performance of linear systems affected by parametric as well as dynamic uncertainty. While exact computation of MU can be prohibitively complex, an efficiently computable upper bound was obtained in [2], yielding a practical sufficient condition for robust stability and performance. In this note, the results of [2] are used to study the case of state space models of the form x{WITH DOT ABOVE IT}=(A_0={SIGMA i=1 to m of DELTA_i * A_i}) where the A_i's are n X n real matrices and the DELTA_i's are uncertain real parameters. The case where the A_i's have low rank is given special attention. When the A_i's all have rank one, (1) is equivalent to the model used by Qiu and Davison [3], which itself generalizes that used by Yedavalli [4]. By means of two examples, we compare our bound to those proposed in [3] and [4].