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In this paper we give an optimal state-space solution to the H − /H ∞ fault-detection (FD) problem for linear time invariant dynamic systems. An optimal H − /H ∞ FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. We provide a state-space realization of the optimal filter in an observer form using the solution of a linear matrix inequalities optimization problem. We also show that, through the use of weighting filters, the detection performance can be enhanced and some assumptions can be removed. Two numerical examples are given to illustrate the algorithm.

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