Further Results on Induced <inline-formula> <tex-math notation="LaTeX">$l_\infty$ </tex-math> </inline-formula> RH FIR Filtering

Abstract

The first results on the induced ${l_\infty }$ receding horizon (RH) finite impulse response (FIR) filtering were obtained by Ahn for a nonsingular system matrix without consideration of external control input, which limited the area of applications. This brief discusses a new design condition for the induced ${l_\infty }$ RH FIR filter applied to model with an arbitrary system matrix and external control input. Based upon this result, a correspondence is found between the induced ${l_\infty }$ RH FIR filter and the ${H_\infty }$ RH FIR filter. Higher robustness of the proposed filter against uncertainties in the system matrix is shown in a comparison with the existing induced ${l_\infty }$ RH filter, which has an infinite impulse response.