-5 -4 -3 -2 -1 0 1 2 3

-2

-1

0

1

2

3

4

Constraints

Iterating

Invariant set

O

Figure 3: Invariant set for closed loop system

-5 -4 -3 -2 -1 0 1 2 3

-2

-1

0

1

2

3

4

Constraints

Iterating

Control Invariant set

-5 -4 -3 -2 -1 0 1 2 3

-2

-1

0

1

2

3

4

Constraints

State and input constraints with LQR

Iterating

Invariant set

⊆

∈ ⇒ ∃ ∈ ∈ ∈