输入带有时滞的线性系统的镇定

考虑带有输入时滞的线性系统的镇定问题.通过把时滞写成一阶传播方程,带有输入时滞的镇定问题转化为常微分方程和一阶双曲方程组成的串联系统的镇定问题.与现有Backstepping方法不同,文章给出了新的变换,其核函数是一阶倒向向量值常微分方程,这使得控制的设计更加简单.文章给出了新的状态反馈控制器,并证明了闭环系统解的适定性和指数稳定性.数值模拟说明,给出的方法是非常有效的.

Stabilization of a Linear System with Input Delay

In this paper,we consider stabilization of a linear system with input delay.By writing the time delay as a transport equation,the stabilization of linear system with time delay is converted into stabilization of a cascade system of a first order hyperbolic equation and an ordinary differential equation.Different from the Backstepping method,the kernel function of the proposed transformation is the first order backward vector-valued ordinary differential equation which simplifies the controller design.A new state feedback controller is given and the well-posedness and the exponential stability are proved.The numerical simulation illustrates that the propose method is quite effective.