Squaring down by static and dynamic compensators

Given a system, which is not necessarily invertible and which has an unequal number of inputs, a method of `squaring down', that is a method of designing pre-compensators and postcompensators such that the resulting system has an equal number of inputs and outputs and is invertible, is presented. The compensators are, in general, dynamic and have the property that the additional finite zeros induced by them are assignable to the open left-half complex plan. Furthermore, the compensators are asymptotically stable, and hence do not deteriorate the robustness and performance of an eventual feedback design. Also, the compensator design preserves the stabilizability, detectability, and minimum-phase properties and the infinite zero structure of the original system. Thus, a method of designing nonsquare systems by converting them to square invertible systems is introduced. Two applications of such a design philosophy, (1) diagonal decoupling with state feedback; and (2) almost disturbance decoupling with output feedback, are pointed out