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Zbl 1125.93489
Pan, Zigang; Liu, Yungang; Shi, Songjiao
Output feedback stabilization for stochastic nonlinear systems in observer canonical form with stable zero-dynamics. (English)
[J] Sci. China, Ser. F. 44, No. 4, 292-308 (2001). ISSN 1009-2757

Summary: In this paper, we study the problem of output feedback stabilization for stochastic nonlinear systems. We consider a class of stochastic nonlinear systems in observer canonical form with stable zero-dynamics. We introduce a sequence of state transformations that transform the system into a lower triangular structure that is amenable for integrator backstepping design. Then we design the output-feedback controller and prove that the closed-loop system is bounded in probability. Furthermore, when the disturbance vector field vanishes at the origin, the closed-loop system is asymptotically stable in the large. With special care, the controller preserves the equilibrium of the nonlinear system. An example is included to illustrate the theoretical findings.

MSC 2000:: *93E15 Stochastic stability
93D15 Stabilization of systems by feedback

Keywords: observer canonical form; integrator backstepping; zero dynamics; asymptotic stability in the large

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