A Converse Theorem for Riemannian Contraction under Uniform Incremental Exponential Stability

Key Points

• The research aims to establish a relationship between uniform exponential stability and the existence of a Riemannian contraction metric.
• Proved a theorem linking exponential stability to Riemannian contraction metrics.
• Constructed the contraction metric using integral Gramian representation.
• Derived explicit bounds on contraction rate and assessed robustness under disturbances.
• Confirmed existence of a Riemannian contraction metric under uniform exponential stability.
• Provided explicit bounds for contraction rates.
• Demonstrated robustness of the metric against bounded disturbances.