Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Aff<strong>in</strong>e sets<br />
Def<strong>in</strong>ition<br />
A subset S of a l<strong>in</strong>ear vector space is aff<strong>in</strong>e if x = αx1 + (1 − α)x2<br />
belongs to S for every x1, x2 ∈ S and α ∈ R<br />
Geometric idea: l<strong>in</strong>e through any two po<strong>in</strong>ts belongs to set<br />
Every aff<strong>in</strong>e set is convex<br />
S aff<strong>in</strong>e iff S = {x | x = x0 + m, m ∈ M} with M a l<strong>in</strong>ear subspace<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 22 / 59
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