Abstract
In this paper, we derive Lyapnov stability theory for rough systems, which are dynamical systems driven by rough paths. To simplify the discussion, we only consider the class of geometric p-rough paths with p? [2,3) that contains some limit processes of periodic inputs and Wiener processes created by some approximation theorems such as McShane and WongZakai's results. The main advantage of the rough path analysis is making Itô maps continuous; hence, the related stability analysis enable us to consider deterministic and stochastic asymptotic stability notions in uniform way. This paper is the first step to show the effectiveness of the rough path anlaysis on stability analysis and stabiliation designs for nonlinear dynamical systems having various unbounded variation signals.
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