Cheap control tracking performance for non-right-invertible systems

A fundamental limitation exists in the achievable tracking performance of non-right-invertible systems. This limitation manifests itself in the cheap control tracking cost, which we show to be a function of the plant non-minimum phase zeros and of the variation with frequency of the plant direction. The cheap control tracking cost is further connected with an integral relation that constrains the performance of any stable closed-loop system where the plant has a single input and two outputs.