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 any given negative value for some of these classes. The classes that admit PID-controllers with this property of small negative real-part assignability of closed-loop poles include stable and some unstable plants.
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Chang, TS., Gündeş, A.N. (2009). MIMO PID Controller Synthesis with Closed-Loop Pole Assignment. In: Ao, SI., Rieger, B., Chen, SS. (eds) Advances in Computational Algorithms and Data Analysis. Lecture Notes in Electrical Engineering, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8919-0_29
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