A discrete-time game theoretic multiple-fault detection filter

In this paper, a previously published discrete-time game theoretic fault detection filter is generalized to the multiple-fault case. The derivation models the detection filter problem as a collection of disturbance attenuation problems, which are optimized via a single cost function. Once solved, the implied discrete-time Riccati inequalities may be used as the constraints of a secondary cost function, which is optimized to find a specific filter gain that achieves secondary objectives. Furthermore, it is shown that the novel detection filter approximates those obtained using spectral and geometric theories, improves their robustness to noise and initial condition errors, and models sensor faults directly rather than requiring that they be rewritten as dynamic faults.