The Electroacoustic absorber is an interesting device for boundary impedance control. In its most efficient configuration, it is composed of a loudspeaker (actuator) whose motion is driven by the electrical current in the speaker coil, based upon the measurement of a quasi-collocated sound pressure on the speaker diaphragm. So far, the corrector transfer function has been mainly synthesized based upon a simple model-inversion approach, proving good performances in various noise control applications such as room modal equalization, noise transmission mitigation and nonreciprocal propagation in acoustic waveguides. Nevertheless, the time delay in the digital control implementation significantly affects both tunability and efficient bandwidth in the model-inversion strategy. In this contribution we provide the H&_infty; synthesis approach for the impedance control problem, showing that it allows to improve the tunability of the Electroacoustic Absorber with respect to classical and model-inversion techniques. First, we formulate the standard problem for the impedance control, then we provide some examples where the H&_infty; can help accomplishing the specifications of performance and acoustical passivity.