State-feedback stabilization for a class of stochastic time-delay nonlinear systems.

*(English)*Zbl 1263.93184Summary: 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 |

##### Keywords:

adding-a-power-integrator technique; stochastic time-delay nonlinear systems; recursive design; state-feedback stabilization; Lyapunov method
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\textit{W. Chen} et al., Int. J. Robust Nonlinear Control 22, No. 17, 1921--1937 (2012; Zbl 1263.93184)

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