Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Optimiser: SeDuMi<br />
Demo no.3<br />
Preprocesor: YALMIP<br />
Let<br />
G( s)<br />
2<br />
s<br />
10<br />
2s<br />
10<br />
The state space representation is<br />
A<br />
2<br />
8<br />
1.25<br />
; B<br />
0<br />
1<br />
; C<br />
0<br />
0<br />
1.25; D<br />
0.<br />
F<strong>in</strong>d norm H 2 and compare it with the result of Matlab ®<br />
function.<br />
KSO materiały do wykładu 2008/09 43<br />
Scope of the lecture<br />
• <strong>Control</strong> – classical vs. modern<br />
• Optimisation approach<br />
• Computer tools support<br />
• LMI primer<br />
• Basic LMI tools for control<br />
• Analysis<br />
• Synthesis<br />
• Conclusions<br />
KSO materiały do wykładu 2008/09 44<br />
Analysis (1)<br />
Robustness problems<br />
1. Robust stability,<br />
2. Robust performance.<br />
Question: what is the biggest admissible Δ ?<br />
G G G 0<br />
( I )<br />
G 0<br />
Δ<br />
Δ<br />
G0<br />
G0<br />
KSO materiały do wykładu 2008/09 45<br />
15
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