PID controller synthesis with shifted axis pole assignment for a class of MIMO systems

For certain classes of linear, time-invariant, multi-input multi-output plants, a systematic synthesis is developed for stabilization using Proportional+Integral+Derivative (PID) controllers, where the closed-loop poles can be assigned to the left of an axis shifted away from the origin. The real-parts of the closed-loop poles can be smaller than the real-part of the largest transmission-zero of the plant. Plant classes that admit PID controllers with this property include stable and unstable multi-input multi-input plants with transmission-zeros in the left-half complex-plane.