Guaranteed gain-phase margins for multi-model control

In the simultaneous performance design problem considered by the authors (1997), linear-quadratic cost function state and control weightings are assumed. A single static state feedback gain is determined which minimizes the guaranteed-cost bound for each of the systems. It is now shown that subject to certain restrictions, the guaranteed-cost gain results in “non-fragile” system control: an infinite increasing gain margin, a decreasing gain margin of 1/2, and phase margins of sixty degrees for each system. The converse is also considered: given a guaranteed-cost gain, the set of all state and control weightings are found for which that gain remains optimal. This is possible through the use of a Kalman matrix identity