Connection between plant zeros and H∞ controller order reduction

The phenomenon of H<sup>∞</sup> controller-pole/plant-zero cancellation is analyzed. Symmetrical descriptor form formulae for the H<sup>∞</sup> central controller are derived and are used to prove controller-pole/plant-zero cancellation in H<sup>∞</sup> design. It is also shown that these particular controller poles are not controllable/observable from the auxiliary compensator/free parameter. This fact is then exploited to find an auxiliary compensator which will produce an internal pole-zero cancellation of s<sub>o</sub> within the H<sup>∞</sup> controller, reducing the order of the controller without affecting the closed loop H<sup>∞</sup> norm.

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