Receding-Horizon $l_{2}{-}l_{\infty}$ FIR Filter With Embedded Deadbeat Property

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.