Abstract
This paper deals with the stochastic stability of a class of nonlinear distributed-parameter systems described by Ito's stochastic partial differential equation. Under appropriate assumptions, the state of the system is expanded into a series of eigenfunctions. By using MKY (Meyer-Kalman-Yakubovich) Lemma, a stochastic Liapunov functional in a form of infinite series is proved to exist, if countably many Popov type conditions are satisfied. Consequently, sufficient conditions are obtained for the system to be asymptotically stable with probability one. Finally an example, which is typical of a physical system, is presented to illustrate the applicability of the main result.
