The Design And Analysis Of Output Feedback Control For Stochastic Nonlinear Systems

In recent years, many researchers have been focused on the stability of deter-ministic nonlinear systems. However, these systems are usually disturbed by outside uncertain factors in real lives, so the works on the stability of stochastic nonlinear systems are significantly important. In this paper, we mainly address two problems: (1) One is to extend the results on the stability of deterministic nonlinear systems to a class of stochastic nonlinear systems via the backstepping method; (2) The other is to combine the backstepping method with the mathematical induction to prove the glob-ally asymptotic stability of a class of stochastic nonlinear systems with time-varying delay by the output feedback control. Firstly, we design a linear output feedback con-trol for a class of stochastic nonlinear systems and use the Lyapunov function to prove globally asymptotic stability of the closed-loop system. Secondly, we use the mathe-matical induction and the back-stepping design method to construct a novel Lyapunov function, as well as to design a linear output feedback control for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable. Then, two examples and their simulations are given to illustrate the theoretical results. Finally, we conclude our work in several remarks and give a discussion for researches in future.