线性连续时变系统H_∞故障检测滤波器设计

Design of H_∞ fault detection filter for linear continuous time-varying systems

将一类线性连续时变系统的基于观测器的故障检测问题归结为H∞滤波问题.将H∞故障检测滤波器设计问题等价为求一类不定二次型的最小值,并使最小值大于零的问题.引入相应的格林空间随机系统,应用格林空间投影理论和新息分析方法,得到了不定二次型的最小值及其存在条件.通过分析不定二次型最小值存在条件和确保不定二次型最小值大于零,给出了H∞故障检测滤波器存在的充要条件,得到了基于微分黎卡提方程的故障检测滤波器参数矩阵.算例验证了所提出方法的有效性.

This paper deals with the problem of observer-based fault detection for a class of linear continuous time-varying systems in the framework of H∞ filtering.First,the design of H∞ fault detection filter is equivalent to that a certain indefinite quadratic form has a minimum and the filter is such that the minimum is positive.Then,by introducing a corresponding Krein space stochastic system and applying projection and innovation analysis,the minimum of indefinite quadratic form and its existence condition are derived.Finally,through analyzing the existence condition of the minimum and guaranteeing the positivity of the minimum,a sufficient and necessary condition of the H∞ fault detection filter is proposed and its parameter matrices based on differential Riccati equation is obtained.A numerical example is given to show the effectiveness of the proposed method.