Linear Matrix Inequalities in Control

Affine functions
Definition
A function f : S → T is affine if
f(αx1 + (1 − α)x2) = αf(x1) + (1 − α)f(x2)
for all x1, x2 ∈ S and for all α ∈ R
Theorem
If S and T are finite dimensional, then f : S → T is affine if and only if
f(x) = f0 + T (x)
where f0 ∈ T and T : T → T a linear map (a matrix).
Siep Weiland and Carsten Scherer (DISC) Linear Matrix Inequalities in Control Class 1 23 / 59