2005/10/13 by Winfried Lohmiller, Jean-Jacques Slotine, Lohmiller, Winfried +1
Engineering · Physics and Astronomy · #Advanced Control Systems Optimization #Advanced Thermodynamics and Statistical Mechanics #Control and Stability of Dynamical Systems #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)
paper · pdf · doi:10.48550/arxiv.nlin/0510025
openalex publication_date 2005/10/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.