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.

The state feedback H_∞ control problem for standard discrete-time singularly perturbed systems with polytopic uncertainties is considered. Two methods for designing H_∞ controllers are given in terms of solutions to a set of linear matrix inequalities, where one of them is with the consideration of improving the upper bound of singular perturbation parameter ε. Moreover, a method of evaluating the upper bound of singular perturbation parameter ε with meeting a prescribed H_∞ performance bound requirement is also given. Numerical examples are given to illustrate the effectiveness of the proposed methods.