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This article is devoted to the global continuous control for stochastic low-order cascade nonlinear systems with time-varying delay and stochastic inverse dynamics. Compared with existing results, the nature of only continuous, but nonsmooth, is unfolded since the power of the stochastic cascade system is of low order; and all the traditional growth conditions on unknown drift and diffusion nonlinearities and local Lipschitz condition are quitted, which largely extends the scope of application. Combining with stochastic input-to-state stability, two new lemmas are developed with rigorous proofs to deal with uncertain nonlinear terms and unmeasurable stochastic inverse dynamics. A continuous control scheme consisting of a delay-independent partial state feedback controller and a serial of dynamic update laws is proposed to guarantee the globally asymptotical stability of the closed-loop system.

Global Stabilization for Stochastic Continuous Cascade Nonlinear Systems Subject to SISS Inverse Dynamics and Time-Delay: A Dynamic Gain Approach