On the Computation of Allowable Bounds for Parametric Uncertainty

The problem of stability analysis of linear systems under parametric uncertainty is considered. The Lyapunov direct method is used to derive allowable upper-bounds on the parameters such that the stability of the perturbed system is guaranteed. An optimisation procedure is used for systematically choosing the best Lyapunov matrix so that the conservation on the upper-bounds is reduced. A `non-conservative´ expression is used in the optimisation procedure, and hence improvements over existing results are obtained. In addition, similarity scaling is shown to be a useful technique to enhance some results.