H∞‐FIR filtering of disturbed systems using LMI under measurement and initial errors

Abstract

SummaryFinite impulse response (FIR) filtering is known to be more robust than Kalman filtering. In this article, we derive a discrete convolution‐based ‐FIR observer for disturbed systems under measurement and initial errors. The gain for the ‐FIR observer is obtained numerically by solving a linear matrix inequality (LMI). Since the LMI has a term that is quadratic with respect to the filter gain, we modify and constrain LMI by introducing an additional variable and proving a theorem. It is shown numerically and experimentally that for disturbed systems operating under measurement and initial errors, the developed ‐FIR observer surpasses the optimal FIR and Kalman filters in accuracy and has almost the same robustness as a robust unbiased FIR filter.