Linear Matrix Inequalities in Control

Examples of convex sets
With a ∈ R n \{0} and b ∈ R, the hyperplane
and the half-space
are convex.
H = {x ∈ R n | a ⊤ x = b}
H− = {x ∈ R n | a ⊤ x ≤ b}
The intersection of finitely many hyperplanes and half-spaces is a
polyhedron. Any polyhedron is convex and can be described as
{x ∈ R n | Ax ≤ b, Dx = e}
for suitable matrices A and D and vectors b, e.
A compact polyhedron is a polytope.
Siep Weiland and Carsten Scherer (DISC) Linear Matrix Inequalities in Control Class 1 18 / 59