Global stabilization via output feedback of stochastic nonlinear time‐delay systems with time‐varying measurement error: A Lyapunov–Razumikhin approach

Abstract The output feedback stabilization for a class of stochastic nonlinear systems in lower‐triangular form is discussed. The key feature of the studied systems is that both of time‐delay factors and sensor measurement error are considered into system modeling. To handle these uncertainties in unmeasured states, a form of full‐order state observer is introduced to rebuild the states of the systems. By developing a simple but efficient control scheme, a linear output feedback controller coupled with two different static gains is designed to stabilize the whole system. In contrast to the conventional Lyapunov–Krasovskii functional approach, a framework of stability analysis based on Lyapunov–Razumikhin function is proposed for the closed‐loop stochastic system. The advantage of the proposed method lies in the superior capability of tackling various types of time delays. Specially, the time derivatives of time‐delay terms can be no less than 1, or even unbounded. Finally, two examples are shown to validate our theoretical results.