A lifted domain-based metric for performance evaluation of LTI and LTV discrete-time tracking controllers

The Frobenius norm of the lifted system representation of tracking error dynamics is proposed as a metric for evaluating the tracking performance of discrete-time linear time invariant (LTI) and linear time varying (LTV) controllers. The proposed metric is introduced here in the context of feedforward tracking control of LTI single-input single-output (SISO) nonminimum phase (NMP) systems, though it is more broadly applicable. It is shown that the filtered basis functions (FBF) approach, an LTV tracking control technique studied by the authors in prior work, is the optimal solution to the rank constrained minimization of the proposed metric. Moreover, for the FBF controller, the metric is independent of plant dynamics, which is not the case for most other tracking controllers; it is also independent of the type of basis functions employed in the FBF controller. The effectiveness of the proposed metric as a tracking performance evaluation tool for both LTI and LTV tracking controllers is demonstrated analytically and numerically on LTI plants with different zero locations.