Receding-Horizon l(2)-l(infinity) 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(infinity) performance with the embedded deadbeat property and is called the FIR l(2)-l(infinity) 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(infinity) 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(infinity) filter.