Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
Linear Matrix Inequalities in Control
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Upper and lower bounds for convex programs<br />
Primal optimization problem<br />
Popt = <strong>in</strong>f<br />
x∈X<br />
f(x)<br />
subject to g(x) ≤ 0, h(x) = 0<br />
Can we obta<strong>in</strong> bounds on optimal value Popt ?<br />
Upper bound on optimal value<br />
For any x0 ∈ S we have<br />
Popt ≤ f(x0)<br />
which def<strong>in</strong>es an upper bound on Popt.<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 33 / 59
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