H ∞ sensitivity minimization using decentralized feedback: 2-input 2-output systems

H∞ norm minimization of the sensitivity and complementary sensitivity functions of 2-input 2-output linear time-invariant finite-dimensional systems using decentralized feedback is considered. It is shown that a set of fixed zeros and a set of fixed poles play a central role in the related minimization problems, and lead to various performance limitations. A comparison between decentralized and centralized controllers in these minimization problems also yields a rigorous characterization of a class of 2-input 2-output plants for which centralized controllers bring no extra benefits compared to decentralized controllers in some special performance objectives.

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