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) systems as well as systems with transmission zeros on the unit circle. Towards this end, first the problem of unknown state and input reconstruction of non-minimum phase systems is addressed. 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 that is designed 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 state and input reconstruction can be achieved by selecting the delay to be sufficiently large. Our proposed inversion scheme is then applied to solve the output-tracking control problem. Furthermore, we have also proposed a methodology to handle the output tracking problem of systems that have transmission zeros on the unit circle in addition to MP and NMP zeros. Simulation case studies are also presented to demonstrate and illustrate the merits and capabilities of our proposed methodologies.