Fault Diagnosis for Non-minimum Phase Systems usingH∞ Optimization

Analysis and design algorithms for residual generators for non minimum phase systems are given. It is shown that H∞ optimization of residual generators applied directly to systems including non minimum phase zeros can be very conservative. To remove this conservatism in theH∞ optimization of the residual generators, a factorization of the non minimum phase system into a minimum phase part and an all-pass factor including the non minimum phase zeros can be applied. The optimization of the residual generator can then be done with respect to the minimum phase part of the system only. It is shown that the effect from the all-pass factor will not affect the 2-norm of the residual vector.