Inversion-Based Output Tracking and Unknown Input Reconstruction of Square Discrete-Time Linear Systems

In this paper, we propose a framework for output tracking control of both minimum phase (MP) and non-minimum phase (NMP) discrete-time linear systems. Towards this end, we first address the problem of unknown state and input reconstruction of non-minimum phase systems. An unknown input observer (UIO) is designed that accurately reconstructs the minimum phase states of the system. The reconstructed minimum phase states serve as inputs to an FIR filter for a delayed non-minimum phase state reconstruction. It is shown that a quantified upper bound of the reconstruction error exponentially decreases as the estimation delay is increased. Therefore, an almost perfect reconstruction can be achieved by selecting the delay to be sufficiently large. The proposed inversion scheme is then applied to the output-tracking control problem. We have also comprehensively addressed and discussed the non-minimum phase dynamics and derived explicit relationships between the system matrices of the above dynamics. Simulation case studies are also presented that demonstrate the merits and capabilities of our proposed methodology.