State Feedback Stabilization for a Class of Upper-Triangular Stochastic Nonlinear Systems with Time-Varying Control Coefficients

Abstract

The problem explored in this article concerns the stability of the state feedback control of the upper-triangular stochastic nonlinear systems whose control coefficients are time-varying. First, the state feedback control of the corresponding nominal system is carried out by utilizing the backstepping technique combined with the appropriate Lyapunov function. Then, low-gain homogeneous domination technology and the efficient coordinate transformation method are adopted to realize the state feedback control of the original system and ensure the global asymptotic stability (GAS) in probability of the system. Finally, an example is given to illustrate the feasibility and correctness of the method.