Receding-Horizon <inline-formula> <tex-math notation="LaTeX">$l_{2}{-}l_{\infty}$</tex-math> </inline-formula> FIR Filter With Embedded Deadbeat Property

Abstract

This brief proposes a new finite-impulse response (FIR) receding-horizon filter for discrete-time linear systems in state space. A solution has l 2 -l ∞ performance with the embedded deadbeat property and is called the FIR l 2 -l ∞ filter (FIRllF). Based on the linear matrix inequality (LMI) and linear matrix equality (LME) formulations, a sufficient condition is found such that the FIRllF ascertains the guaranteed l 2 -l ∞ performance with the deadbeat property. Using this result, we further obtain a new LMI condition for the existence of the FIRllF without using the LME. Through a numerical example, the proposed FIRllF is shown to be more robust against unexpected uncertainties than the existing l 2 -l ∞ filter.