This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such as H − /H ∞ , H 2 /H ∞ , and H ∞ /H ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal) but useless fault-detection filters.

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An iterative design algorithm is developed for robust disturbance–rejection control of uncertain systems with time-varying parameter perturbations in this paper. For more design degrees of freedom, a generalized equivalent-input-disturbance estimator is adopted to approximate the effect of both disturbances and uncertainties. By the bound real lemma, the H∞ norm is used to evaluate the robust disturbance–rejection performance of the closed-loop uncertain system. To avoid the constraints introduced by the widely used commutative condition, the control gains are divided into two groups and calculated by steps. Further, two robust quadratic stability conditions are derived, and an iterative design algorithm is developed to optimize the robust H∞ disturbance–rejection performance. Finally, the effectiveness and advantages of the developed method are demonstrated by a case study of a suspension system of modern vehicles.

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