An important property of non-minimum-phase multiple-input-multiple-output feedback systems

The non-minimum-phase (NMP(property is easily determined from the requirement that the plant input is bounded. In the single-input-single-output (SISO) system, a right-half-plane (RHP) plant zero at s = b constrains the system transfer function to have a zero at b. Also, the available feedback benefits are significantly restricted. The n × n multiple-input-multiple-output (MIMO) system is NMP if the plant determinant Δhas any RHP zeros, say b_i i=1,…N. The resulting constraint is (formula presented) where Δ_iα(S) is the iα cofactor of the plant transfer matrix and T=[t_ij is the closed-loop system transfer matrix. It has been thought that all n²t_ij (and the n₂ plant disturbance response function l_ij^d), must suffer from the NMP liability in their feedback properties. It is shown that only one row of (formula presented) need so suffer, with a any fixed integer in [1, n].The remaining n(n — 1) elements can be completely free of the NMP liability. A mathematically rigorous synthesis technique previously developed for MP systems is shown to be well suited for precise numerical design for such NMP MIMO plants with significant uncertainties. In this technique, the MIMO design problem is converted into a number of equivalent SISO problems. An example involving disturbance attenuation in a highly uncertain 2×2 NMP plant is included.