In this paper, the exponentially stable problem is discussed for a class of stochastic strict feedforward nonlinear systems. Firstly, by employing the proper coordinate transformation and the novel parameter-dependent controller, the initial stochastic strict feedforward nonlinear system is converted to an equivalent system. After that, the implementable parameter-dependent controller, which is adopted to handle the nonlinearities, can be achieved by reasonably selecting the designed parameter. Finally, by means of stochastic Lyapunov stability theory, it is rigorously verified that the proposed parameter-dependent state-feedback controller and parameter-dependent output-feedback controller can guarantee that the stochastic closed-loop system is the fourth moment exponentially stable. Simulation results demonstrate the efficiency of the proposed parameter-dependent controller.

本文讨论了一类随机严格前馈非线性系统的指数稳定问题。首先，通过适当的坐标变换和新颖的参数相关控制器，将初始随机严格前馈非线性系统转化为等效系统。之后，可以通过合理选择设计参数来实现用于处理非线性的可实现参数依赖控制器。最后，通过随机Lyapunov稳定性理论，严格验证了所提出的参数相关状态反馈控制器和参数相关输出反馈控制器能够保证随机闭环系统是四阶矩指数稳定的。