Robust stability of linear stochastic systems with distributed parameter

Based on the stochastic Fubini theorem, an average Lyapunov functional with regard to spatial variables is constructed, by using Ito formula; the problem of robust exponential stability for a class of linear stochastic system with distributed parameter is investigated. The sufficient conditions for robust exponential stability and almost surely exponential stability are obtained. The corresponding results are also generalized to semi-linear systems.