On the application of a frequency domain controller design methodology to non-minimum phase and unstable systems

A frequency-domain design methodology was developed for controller synthesis maximizing the allowable size of an unknown-but-bounded disturbance while satisfying prespecified control and output constraints. The design technique, which accounts for bandwidth limitations, is based on mapping time-domain constraints into the frequency domain. Application of this technique to non-minimum-phase and/or unstable systems is presented. A non-minimum-phase, unstable SIMO (single-input/multiple-output) system is examined, and the results are compared to those obtained by the set-theoretic (ST) approach. The comparison shows that this methodology can yield controllers that reject step disturbances larger than those obtained by the ST method.