Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Why is convexity <strong>in</strong>terest<strong>in</strong>g ???<br />
Reason 2: uniform bounds<br />
Theorem<br />
Suppose S = co(S0) and f : S → R is convex. Then equivalent are:<br />
f(x) ≤ γ for all x ∈ S<br />
f(x) ≤ γ for all x ∈ S0<br />
Very <strong>in</strong>terest<strong>in</strong>g if S0 consists of f<strong>in</strong>ite number of po<strong>in</strong>ts, i.e,<br />
S0 = {x1, . . . , xn}. A f<strong>in</strong>ite test!!<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 26 / 59
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