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Stochastic contraction analysis is a recently developed tool for studying theglobal stability properties of nonlinear stochastic systems, based on adifferential analysis of convergence in an appropriate metric. To date,stochastic contraction results and sharp associated performance bounds havebeen established only in the specialized context of state-independent metrics,which restricts their applicability. This paper extends stochastic contractionanalysis to the case of general time- and state-dependent Riemannian metrics,in both discrete-time and continuous-time settings, thus extending itsapplicability to a significantly wider range of nonlinear stochastic dynamics.

Stochastic Contraction in Riemannian Metrics