Controller Design and Stability Analysis for a Class of Leader-Type Stochastic Nonlinear Systems

In this paper, the non-scaling backstepping approach is used to examine the controller design process and stability analysis of a class of leader-type stochastic nonlinear systems. By utilizing the non-scaling backstepping design method and Lyapunov method, the controller of the leader-type stochastic nonlinear system is derived. Different from the previous literature on controller design, we develop a more computationally efficient way for designing controllers because the scaling function in the coordinate transformation is not included. Meanwhile, the prescribed-time mean-square stabilization on the equilibrium and two important estimates are derived by combining the Lyapunov method with the matrix norm. Compared to the finite-time stabilization in other studies, the prescribed-time stabilization can determine the convergence time without relying on the initial value and has more real-world applicability. To illustrate the effectiveness of the controller derived in this paper, numerical examples are provided finally.