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 />
Examples: saturation constra<strong>in</strong>ts, safety marg<strong>in</strong>s, physically<br />
mean<strong>in</strong>gful variables, constitutive and balance equations all assume<br />
the form S.<br />
l<strong>in</strong>ear program:<br />
f(x) = c ⊤ x, g(x) = g0 + Gx, h(x) = h0 + Hx<br />
quadratic program:<br />
f(x) = x ⊤ Qx, g(x) = g0 + Gx, h(x) = h0 + Hx<br />
quadratically constra<strong>in</strong>t quadratic program:<br />
f(x) = x ⊤ Qx+2s ⊤ x+r, gj(x) = x ⊤ Qjx+2s ⊤ j x+rj, h(x) = h0+Hx<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 32 / 59
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