Abstract
For discrete-time plants with direct feedthrough terms, we consider a loop transfer recovery (LTR) technique based on the Riccati equation formalism. We find that the recovery procedure at the plant input side should utilize the correlation between a disturbance and an observation noise. The variance of the observation noise component independent of the disturbance is taken as a parameter for the recovery. It should be noted that most discrete-time models of practical interest are non-minimum phase. We show that, for non-minimum phase plants, the Riccati equation with the parameter being zero has multiple non-negative definite solutions one of which is stabilizing. The stabilizing solution is then used to obtain an explicit expression of the sensitivity matrix achieved by the recovery procedure. Using the expression, we discuss the meaning of the LTR for non-minimum phase plants with direct feedthrough terms.
