3
Nonlinear convex inequalities can be converted to LMI form using Schur
complements.
Schur Complenment
Q
(a) T
S
S
>0
R
if and only if
and Q − SR −1S T > 0 .
R>0
Q
(b) T
S
S
>0
R
if and only if
Q>0
Proof:
(4.3a)
and R − S T Q −1S > 0 .
(4.3b)
