Abstract:

This paper is devoted to solvingthe global stabilization problem viastatefeedback and adaptive technique for a class of uncertain highorder stochastic nonlinear systems. Although much effort has been made for deterministic ones, the problem is significant and deserves attention since it involves the effects caused by the stochastic disturbance and, for which, an appropriate control Lyapunov  function should be twice continuously differentiable and hence is moredifficult to find. By introducing a novel control Lyapunov  function and using the method of adding a power integrator, an adaptive statefeedback continuous controller is successfully designed, which guarantees that the original system states are globally asymptotically stable in probability while the other closedloop signals are globally stable in probability. A simulation example is provided to illustrate the effectiveness of the proposed approach. 

Key words: stochastic nonlinear systems; nonlinear parameterization; global stabilization; adaptive technique; adding a power integrator