  Nonlinear contraction theory is a comparatively recent dynamic control system
design tool based on an exact differential analysis of convergence, in essence
converting a nonlinear stability problem into a linear time-varying stability
problem. Contraction analysis relies on finding a suitable metric to study a
generally nonlinear and time-varying system. This paper shows that the
computation of the metric may be largely simplified or indeed avoided
altogether by extending the exact differential analysis to the higher-order
dynamics of the nonlinear system. Simple applications in economics, classical
mechanics, and process control are described.
