When the lateral dimensions of a duct is larger than or comparable to the wavelengths of Interest, higher order modes propagate in the duct. These modes will be radiated and produce noise. A number of sensors and actuators for control of radiating noise from the duct have to be incorporated with the number of modes which one wants to control. These considerations motivated the present study that considers a control system which has less microphones and control sources than required. In this work, by theoretical analysis, the control performance of such a kind of system is investigated in terms of sound-field variables and control system variables. The possible maximum and minimum value. mean and variance of residual acoustic potential energy are derived for the set of primary sound fields.