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Zbl 1127.93354
Xie, Xue-Jun; Tian, Jie
State-feedback stabilization for high-order stochastic nonlinear systems with stochastic inverse dynamics. (English)
[J] Int. J. Robust Nonlinear Control 17, No. 14, 1343-1362 (2007). ISSN 1049-8923

Summary: For a class of high-order stochastic nonlinear systems with stochastic inverse dynamics which are neither necessarily feedback linearizable nor affine in the control input, this paper investigates the problem of state-feedback stabilization for the first time. Under some weaker assumptions, a smooth state-feedback controller is designed, which ensures that the closed-loop system has an almost surely unique solution on $[0, \infty)$, the equilibrium at the origin of the closed-loop system is globally asymptotically stable in probability, and the states can be regulated to the origin almost surely. A simulation example demonstrates the control scheme.

MSC 2000:: *93D15 Stabilization of systems by feedback
93E03 General theory of stochastic systems
93C10 Nonlinear control systems

Keywords: stochastic nonlinear systems; stochastic inverse dynamics; state-feedback; stabilization

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