H∞ filter design for delta operator formulated systems with low sensitivity to filter coefficient variations

The problem of designing H_∞ filters for delta operator formulated systems with low sensitivity to filter coefficient variations is investigated. The delta operator provides a theoretically unified formulation of continuous-time and discrete-time systems and also has the advantage of better numerical properties at high sampling rates. In addition to the standard H_∞ criterion, the H_∞ norm of the sensitivity function is introduced in order to improve the designed filter´s insensitivity to the filter coefficient variations. Finsler´s Lemma is used to derive novel sufficient conditions which are adapted to treat this multiplicative objective optimisation problem in a potentially less conservative framework. Linear matrix inequality conditions are obtained for the existence of admissible filters with respect to additive/multiplicative coefficient variations based on two different types of sensitivity measures. Finally, the effectiveness of the proposed method is illustrated by a numerical example. It is shown that the delta operator approach offers better coefficient sensitivity than the traditional shift operator approach when the sampling rate is high.