Higher-Order Nonlinear Contraction Analysis

Winfried Lohmiller; Jean-Jacques E. Slotine

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arXiv · nlin/0510025

Higher-Order Nonlinear Contraction Analysis

Winfried Lohmiller·Jean-Jacques E. Slotine

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Abstract

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.

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Winfried Lohmiller, Jean-Jacques E. Slotine. 2005-10-13. Higher-Order Nonlinear Contraction Analysis. https://arxiv.org/abs/nlin/0510025

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