In this article, we study the controller design and stability analysis for a class of stochastic cascade nonlinear systems with external disturbances. The unmeasurable external disturbance is viewed as an extended state. In order to estimate the unmeasurable system states and the external disturbance, a new extended state observer (ESO) based on the Riccati differential equation is constructed.The stochastic inverse dynamics, the error dynamics of observer, and the ESO constitute new stochastic nonlinear systems. Based on these new systems, an adaptive output feedback controller is proposed by combining stochastic input-to-state stability with backstepping design technique. In stability analysis, it has been shown that the designed controller can guarantee that all closed-loop system signals are almost surely bounded and the original system states are globally asymptotically stable in probability. Finally, a simulation example is given to the validity of the proposed method.

This paper considers the output‐feedback controller for a class of stochastic cascade nonlinear systems with stochastic integral input‐to‐state stable inverse dynamics, unknown control coefficients, and matching disturbances. By augmenting the existing disturbance as an extended state, a novel extended state observer (ESO) is constructed based on the Riccati differential equation. Based on the techniques of Nussbaum function and backstepping, an adaptive output feedback controller is proposed to guarantee that all system states of the resulting closed‐loop system are globally asymptotically stable in probability. Meanwhile, the other signals are almost surely bounded. Additionally, the validity of the proposed control method is verified by simulation examples.

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