# Read e-book online A Course in H∞ Control Theory PDF

By Prof. Bruce A. Francis (eds.)

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**Extra info for A Course in H∞ Control Theory**

**Example text**

Exercise 1. In Figure 4 suppose G (s) = - . Consider a controller of the form s (s-l) K= -Q 1-GQ where Q is real-rational. Find necessary and sufficient conditions on Q in order that K 41 Ch. 4 stabilize G. 5 Closed-Loop Transfer Matrices Now we return to the standard set-up of Figure 1, Chapter 3. 1 gives every stabilizing K as a transformation of a free parameter Q in RH**. The objective in this section is to find the transfer matrix from w to z in terms of Q. In the previous section we dropped the subscripts on G22; now we must restore them.

Then

2 says that its norm also equals IIF[I~. 2, AFH 2 c H 2 . The converse is true too: if AFH2CH2, then F ~ H~. ) Example 4. This is the time-domain analog of the previous example. Recall that convolution in the time-domain corresponds to multiplication in the frequency-domain. Suppose F (s) is a matrix-valued function which is analytic in a vertical strip containing the imaginary axis and which belongs to L , . Taking the region of convergence to be this strip, let f (t) denote the inverse bilateral Laplace transform of F(s).