Stabilization of a class of stochastic feedforward uncertain systems via time-varying state feedback

This paper is devoted to the stabilization problem for a class of stochastic feedforward nonlinear systems with unknown growth rate by time-varying state feedback. As the first contribution, a general LaSalle-type theorem is established for stochastic time-varying systems with the aid of the generalized weakly positive definite function. Then a time-varying state feedback control scheme is established for a class of stochastic feedforward systems with uncertainties in the unknown growth rate. Via the established LaSalle-type theorem, it is shown that all signals of the resulting closed-loop system converge to zero almost surely. A numerical example is presented to demonstrate the validity of the theoretical results