Weakly and strongly non-minimum phase systems: properties and limitations

In this paper, a new classification of non-minimum phase systems based on stabilisability of the internal dynamics is introduced. According to this classification, the non-minimum phase systems are categorised as follows: (1) weakly non-minimum systems, for which a finite value of minimum norm of the regulation error can be obtained, and (2) strongly non-minimum phase systems for which this minimum norm of the regulation becomes infinite due to the presence of both transient and steady-state errors while for the weakly non-minimum phase systems there is no steady-state regulation error. It is worth mentioning that based on this new classification a level of non-minimum phase-ness can be further defined for any given desired trajectory. Furthermore, some numerical simulations are carried out to show consistency with theoretical analysis.