Summary This paper studies the finite‐time stabilizing control problem for a class of switched stochastic nonlinear systems (SSNSs) in p‐normal form. The switched systems under consideration possess the powers of different positive rational numbers and the dead‐zone input nonlinearities. Based on the improving finite‐time stability theorem for SSNSs established in this paper, a general framework to address common state feedback for SSNSs is developed by adopting the common Lyapunov function–based adding a power integrator technique. It is proved that the proposed controller renders the trivial solution of the closed‐loop system uniformly finite‐time stable in probability under arbitrary switchings. Finally, simulation results are given to confirm the validity of the proposed approach.

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a b s t r a c tThis paper investigates the problem of adaptive stabilization control design for a class of high order nonholonomic systems in power chained form with strong nonlinear drifts, including unmodeled dynamics, and dynamics modeled with unknown nonlinear parameters. A parameter separation technique is introduced to transform the nonlinear parameterized system into a linear-like parameterized system. Then, by the use of input-state scaling technique and adding a power integrator backstepping approach, an adaptive state feedback controller is obtained. The adaptive control based switching strategy is proposed to eliminate the phenomenon of uncontrollability. Global asymptotic regulation of the closed-loop system states and the boundedness of other signals are guaranteed. Simulation examples demonstrate the effectiveness of the proposed scheme.

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