Robustness Analysis based on Passivity

A new technique of robust stability analysis for multivariable control systems is introduced in this paper. Existing tools in the literature are mostly based on small gain type of conditions (such as the H¿-norm, ¿ measure etc.). In contrast, the approach presented here is motivated by passivity theory. The natural energy Lyapunov function associated with a passive system allows robustness to be analyzed with Lyapunov stability theory. Consequently nonlinear and time varying perturbations can be considered within the same framework. For unstructured uncertainties, the robustness margin is characterized in terms of an index related to the Hermitian part of a transfer function. If the uncertainties contain additional diagonal structure, stability margins are obtained for variations of each uncertain block in both positive and negative direction. Applications of this robustness analysis technique are illustrated in several examples.