TABLE OF CONTENTS The following sections cover the computer algorithms used in developing the work contained within this book.
Using the formulation for the H ? optimization problem from Chapter 3, Section II, the optimal H ? norm and the optimal or suboptimal H ? controller can be computed. It is assumed that D 12 is of full column rank, and that D 21 is of full row rank. The inputs and outputs are scaled so that the assumptions D 21 = [0 I] and D 12 = [0 I] T are satisfied.13
Step 1: Compute the singular value decomposition for D 12 (see Ref. 9).
| (8.1) |  |
Define:
| (8.2) |  |
and
| (8.3) |  |
Then:
| (8.4) |  |
Step 2: Compute the singular value decomposition for D 21 (see Ref. 9).
| (8.5) |  |
Define:
| (8.6) |  |
and
| (8.7) |  |
Then:
| (8.8) |  |
Step 3: Scale the inputs and outputs.56
Define the scaled inputs v s, u s, and the new outputs z s, y s as follows:
| (8.9) |  |
| (8.10) |  |
| (8.11) |  |
| (8.12) |  |
The new generalized plant G( s) (i.e., the transfer function from [ 
] to [ 
] has the following state space realization:
| (8.13) |  |
where
| (8.14) |  |
| (8.15) |  |
| (8.16) |  |
| (8.17) |  |
| (8.18) |  |
| (8.19) |  |
| (8.20) |  |
| (8.21) |  |
| (8.22) |  |
An optimal (or suboptimal) controller is then generated based on the scaled generalized plant G( s). By definition, this controller has...
