
Chapter 6 Tutorial
Xmath Model Reduction Module 6-2 ni.com
A minimal realization in modal coordinates is C(sI –A)–1B where:
The specifications seek high loop gain at low frequencies (for performance) 
and low loop gain at high frequencies (to guarantee stability in the presence 
of unstructured uncertainty). More specifically, the loop gain has to lie 
outside the shaded region shown in Figure 6-1.
Figure 6-1.  Loop Gain Constraints
A diag 
01
00
0.015–0.765
0.765–0.015–
0.028–1.410
1.410–0.028–
0.04–1.85
1.85–0.04–
,,,
⎩⎭
⎨⎬
⎧⎫
=
B
0.026
0.251–
0.033
0.886–
4.017–
0.145
3.604
0.280
=C′
0.996–
0.105–
0.261
0.009
0.001–
0.043–
0.002
0.026–
=
40 dB/decadeFrequency (rad/sec)