Stability of stationary linear stochastic differential systems controlled by rough paths with Holder exponents greater than 1/3

There are proved stability and asymptotic stability criteria for linear rough path differential systems controlled by rough signals with Holder exponent greater than $1/3$. We obtain sufficient conditions of stability in probability and asymptotic stability in probability of stochastic linear rough path differential equations controlled by rough signals with Holder exponent greater than $1/3$.