State-feedback stabilization for high-order stochastic nonlinear systems without strict triangular conditions

For a class of high-order stochastic nonlinear systems which are neither necessarily feedback linearizable nor affine in the control variables without the strict triangular conditions, this paper studies the problem of state-feedback stabilization for the first time. The main contribution of this paper is the development of a systematic design approach for stochastic nonlinear systems in the absence of triangular conditions. This methodology enables us to remove the strict triangular conditions which have been the common assumption for global stabilization, and leads to a new result combining and generalizing the previous work. Finally, an illustrative example is provided to demonstrate the effectiveness of the proposed control design methodology.