基于LMI的H∞未知输入观测器设计

H∞ Unknown Input Observer Design Based on LMI

摘要:

针对同时具有未知输入和量测噪声的离散Lipschitz非线性系统，采用扩展状态向量的方法将量测噪声向量当作系统状态，从而将系统化为形式上不含量测噪声的广义离散非线性系统.通过设计广义系统H∞未知输入观测器，同时估计出原系统状态和量测噪声.为了降低设计的保守性，将观测器设计转化为线性矩阵不等式(LMI)求解问题，给出观测器设计算法，并基于延迟估计的思想提出一种未知输入代数重构方法.仿真结果表明：提出的方法可以使状态估计、量测噪声及未知输入的重构信号逼近实际信号，证明了该方法的有效性和正确性.

关键词:离散非线性系统;H∞观测器;线性矩阵不等式(LMI);量测噪声重构;未知输入重构

Abstract:

The original discrete time Lipschitz nonlinear system with measurement noise and unknown input is transformed into an augmented descriptor system without measurement noise by taking measurement noise vector as an extended state vector. An H∞ unknown input observer which can estimate the state and the measurement noise of original system is developed, and the existence of the observer depends on the solution of the feasible solutions of linear matrix inequality (LMI). Then, an algebraic unknown input reconstruction method is proposed based on the delay estimation approach. The result of a simulation example is given to illustrate the effectiveness and correctness of the proposed method.

Key words:discrete time nonlinear system; H∞ observer; linear matrix inequality (LMI); measurement noises reconstruction; unknown input reconstruction