Applications of contraction analysis

Contraction analysis derives new results in nonlinear system analysis using methods inspired from fluid mechanics and differential geometry. Elementary continuum tools are recast in a general system context and lead to a differential convergence analysis, which may be viewed as a generalization of the classical Krasovkii theorem and, more loosely, of linear eigenvalue analysis. One feature is that convergence and limit behavior are in a sense treated separately, leading to significant conceptual and design simplification. After reviewing the approach, this paper details how it can be applied to globally convergent observer designs for nonlinear mechanical systems, and briefly discusses other potential applications.