Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Simple examples of LMI’s<br />
1 + x < 0<br />
1 + x1 + 2x2 < 0<br />
<br />
1<br />
0<br />
<br />
0 2<br />
+ x1<br />
1 −1<br />
<br />
−1 1<br />
+ x2<br />
2 0<br />
<br />
0<br />
≺ 0.<br />
0<br />
All the same with ≻ 0, 0 and 0.<br />
Only very simple cases can be treated analytically.<br />
Need to resort to numerical techniques!<br />
Siep Weiland and Carsten Scherer (DISC) <strong>L<strong>in</strong>ear</strong> <strong>Matrix</strong> <strong>Inequalities</strong> <strong>in</strong> <strong>Control</strong> Class 1 42 / 59