A matrix factorization solution to the H-/H∞H-/H∞ fault detection problem

In this paper we give a matrix factorization solution to the H-/H∞H-/H∞ fault detection (FD) problem for linear time invariant dynamic systems. An H-/H∞H-/H∞ FD filter minimizes the sensitivity of the residual signal to disturbances while maintaining a minimum level of sensitivity to faults. More specifically, it minimizes the largest singular value, over the extended imaginary axis, of the transfer matrix from the disturbance to the residual signal vectors subject to the constraint that the singular values of the transfer matrix from the fault to the residual vectors are larger than or equal to 1. We show, through the use of matrix function factorizations and completions, that the problem reduces to a nonstandard model matching problem which is then solved under a mild assumption concerning the rank of a matrix function. We also give an illustrative example.