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Improved backstepping control for stochastic high-order nonlinear time delay system with a constructive mechanical system

In this paper, the backstepping control problem is addressed by backstepping technique for a class of high-order stochastic nonaffine nonlinear systems. Different from existing papers, the nonlinear vector terms of system depend on the unmeasurable states besides the measurable output, and replace the high order index from constant value to varying value in order to allow the result to apply to the more general situations. The maximum value interval of observer gain parameter is chosen to ensure the closed-loop system globally asymptotically stable in probability. The efficiency of the output-feedback controller is illustrated by a hydraulic mechanical system simulation.