Stochastic input-to-state stability and applications to global feedback stabilization

Notions of stochastic input-to-state stability are introduced and their Lyapunov characterizations are established. These notions constitute extensions of the deterministic ISS proposed by E. Sontag and are used to derive sufficient conditions for global stabilization for triangular stochastic systems by means of output-and bounded - static feedback, as well as by dynamic feedback controller.