Fault diagnosis for non-minimum phase systems using ℋ∞ optimization

The analysis and design algorithms for residual generators for nonminimum phase systems are given. It is shown that the ℋ_∞ optimization of residual generators applied directly to systems including nonminimum phase zeros can be very conservative. To remove this conservatism in the ℋ_∞ optimization of the residual generators, a factorization of the nonminimum phase system into a minimum phase part and an all-pass factor including the nonminimum 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