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Summary: In this paper, we give some new results on finite‐time stabilization for stochastic nonlinear systems whose powers of integrators are all positive odd rational numbers (ie, numerators and denominators of the powers are all positive odd integers) but not necessary only high order or low order. By adopting new conditions on drift and diffusion terms, Lyapunov function, and controller design method, a state feedback controller is designed to guarantee stochastic nonlinear systems finite‐time stable in probability. Moreover, when unknown parameters exist in systems, we give the adaptive finite‐time state feedback controller. Numerical examples demonstrate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates adaptive state feedback stabilization for a class of more general stochastic high‐order nonholonomic systems. By constructing the appropriate Lyapunov function, skillfully combining parameter separation, sign function, and backstepping design methods, an adaptive state feedback controller is designed to eliminate the phenomenon of uncontrollability and guarantee global asymptotic stability in probability of the closed‐loop system. Two simulation examples are used to demonstrate the effectiveness of this method. [ABSTRACT FROM AUTHOR]

This paper focuses on global adaptive state-feedback stabilization for a class of high-order uncertain nonlinear systems with multiple delays. Restriction on system growth is relaxed. Two dynamic gains are introduced to deal with uncertainty and nonlinear growth rate of the system. Without precise information about time-delay being needed and only by like Lyapunov function, a new control strategy is presented based on homogeneous domination idea and two necessary transformations. As an application, the developed scheme is utilized to control design of a two-stage chemical reactor with delayed recycle streams. Copyright © 2014 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]