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2.5. µ SYNTHESIS AND D-K ITERATION 59
Figure 2.11: The generic interconnection structure for synthesis
F
u
(F
l
(P(s),K(s)),∆)
∞
≤ 1. This is equivalent to K(s) satisfying
µ[F
l
(P(s),K(s))] < 1. In other words, the closed loop system satisfies the robust
performance specification.
Unfortunately this problem has not yet been solved, except is a few special cases. The
current approach to this problem, known as D-K iteration, involves the iterative
application of the H
∞
design technique and the upper bound µ calculation. We will give
a brief conceptual overview here and give more algorithmic details in Section 2.5.2.
Consider applying H
∞
synthesis to the full P(s) interconnection structure for this
problem. Suppose that this gives a controller, K(s) such that K(s) stabilizes P(s)and
F
l
(P(s),K(s))
∞
≤ 1.