基于小增益和Lipschitz条件的闭环EIV系统稳定性分析

Stability analysis of closed-loop EIV system based onsmall gain and Lipschitz condition

研究了带有输入扰动和输出扰动的闭环变量带误差系统的稳定性分析。针对一个闭环变量带误差系统,无论是线性还是非线性,可以将其模型看成反馈互联系统,闭环变量带误差系统的扰动项视为反馈互联系统的输入,然后利用小增益定理判断反馈互联系统的有限增益L稳定,从而判断闭环变量带误差系统的稳定性。同时,也给出了使用Lipschitz条件的方法推导并判断系统的稳定性。最后,使用数值仿真验证理论结果。

In this paper,the stability analysis of closed-loop errors-in-variables(EIV)systems with input and output disturbances is studied.For a closed-loop errors-in-variables system,whether linear or nonlinear,its model can be regarded as a feedback interconnec-ted system.The disturbance term of the closed-loop errors-in-variables system is regarded as the input of the feedback interconnected system,and then the small gain theorem is used to judge the finite gain L stability of the feedback interconnected system,so as to judge the stability of the closed-loop errors-in-variables system.Meanwhile,the method of using Lipschitz condition to deduce and judge the stability of the system is also given.Finally,numerical simulation is used to verify the theoretical results.