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And system output can be regulated in probability to a small neighborhood of the equilibrium point with preset precision.
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Meanwhile the system output can be regulated to a small region in probability with preset precision within finite time.
It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability.
The closed-loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely.
In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin.
Based on the backstepping design method and homogeneous domination technique, the closed-loop system can be proved to be globally stable in probability and the states can be regulated to the origin almost surely.
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