${\cal H}_{\infty}$ Output-Feedback Control Based on an FIR-Type Quasi-Deadbeat Observer

This technical note proposes a novel output-feedback control law based on a finite impulse response (FIR)-type quasi-deadbeat observer for linear systems. For nominal systems without disturbances, this technical note first establishes the deadbeat condition that reduces the state estimation error to zero within a finite time and verifies that all the hidden poles of the closed-loop system under the quasi-deadbeat observer-based control law are zero and that the separation principle holds true. In order to enhance the disturbance rejection capability for systems with random-work disturbances, on the structural merit of the FIR-type observer, we have proposed the conditions for an
H

_infin
quasi-deadbeat observer and an
H

_infin
stabilizer based on the predetermined observer, respectively.