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State-feedback stabilization for a class of stochastic time-delay nonlinear systems. (English) Zbl 1263.93184
Summary: This paper investigates the problem of state-feedback stabilization for a class of lower-triangular stochastic time-delay nonlinear systems without controllable linearization. By extending the adding-a-power-integrator technique to the stochastic time-delay systems, a state-feedback controller is explicitly constructed such that the origin of closed-loop system is globally asymptotically stable in probability. The main design difficulty is to deal with the uncontrollable linearization and the nonsmooth system perturbation, which, under some appropriate assumptions, can be solved by using the adding-a-power-integrator technique. Two simulation examples are given to illustrate the effectiveness of the control algorithm proposed in this paper.

MSC:
93D15 Stabilization of systems by feedback
93E12 Identification in stochastic control theory
93E03 Stochastic systems in control theory (general)
93C10 Nonlinear systems in control theory
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