Directional Input Analysis for Multivariable Feedback Design

A simple method for analysing directional properties of input mapping is proposed. The method allows the designer to analyse and select an appropriate set of input variables for controller synthesis. The following bounds are derived from a suitable representation of the transfer function: an upper bound for the minimal singular value of the plant transfer function as well as two lover bounds, for the plant condition number and the maximal magnitude of the closed-loop transfer function relating output disturbances to plant inputs. These bounds are shown to be directly related to the value of the smallest singular value of the transformed input matrix.