A Tutorial on Incremental Stability Analysis using Contraction Theory

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.

Keywords

• Contraction theory
• exponential stability
• incremental stability
• Lyapunov stability