“A Tutorial on Incremental Stability Analysis using Contraction Theory”

Authors: Jerome Jouffroy and Thor I. Fossen,
Affiliation: University of Southern Denmark, NTNU, Department of Engineering Cybernetics and NTNU, Centre for Ships and Ocean Structures
Reference: 2010, Vol 31, No 3, pp. 93-106.

Keywords: Contraction theory, exponential stability, incremental stability, Lyapunov stability, methodology

Abstract: This paper introduces a methodology for differential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998). The methodology includes four distinct steps: the descriptions of two systems to be compared (the plant and the observer in the case of observer convergence analysis, the plant and the controller in the case of tracking controller analysis), the definition of an abstract system common to the two systems and denoted as the ´virtual system´, and the convergence study of the virtual system using its virtual dynamics representation. The approach is illustrated on several simple examples.

PDF PDF (678 Kb)        DOI: 10.4173/mic.2010.3.2

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  title={{A Tutorial on Incremental Stability Analysis using Contraction Theory}},
  author={Jouffroy, Jerome and Fossen, Thor I.},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}