Finite-Time Stabilization of High-Order Stochastic Nonlinear Systems With Asymmetric Output Constraints

This article addresses the problem of finite-time stabilization for a class of high-order nonlinear stochastic systems with asymmetric output constraints. A novel barrier Lyapunov function (BLF) is first presented to handle such asymmetric constraints. Further, based on the proposed BLF and the adding a power integrator technique, a controller design approach is developed by the backstepping method. It can be rigorously proved that the designed controller can not only make the system states finite-time converge to the origin in probability but also ensure that the constraint on system output is not violated. Another novelty of this approach is that it is a unified tool owing to its simultaneous application to the systems without output constraints. Finally, the validity of the proposed scheme can be verified by a simulation example.