Non-uniqueness of robust H∞ decentralized PI-control

In the paper we use as an example the control of identical processes operating in parallel. Such systems are quite common in industry, for example in distribution networks or when parallel units (reactors, heat exchangers, etc.) are used. When performance is measured in terms of the H_∞ norm then the optimal single-loop PI or PID-tunings are not necessarily equal for the individual loops. The same applies when model uncertainty is included and the structured singluar value μis used as a performance measure. This is contrary to what one intuitively would expect, and also implies that the optimal solution is non-unique.