Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Examples of convex functions<br />
Convex functions<br />
f(x) = ax 2 + bx + c convex if<br />
a > 0<br />
f(x) = |x|<br />
f(x) = x<br />
f(x) = s<strong>in</strong> x on [π, 2π]<br />
Non-convex functions<br />
f(x) = x 3 on R<br />
f(x) = −|x|<br />
f(x) = √ x on R+<br />
f(x) = s<strong>in</strong> x on [0, π]<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 21 / 59