diff --git a/src/Utils/normalization.jl b/src/Utils/normalization.jl
index 71266aaf..3a800416 100644
--- a/src/Utils/normalization.jl
+++ b/src/Utils/normalization.jl
@@ -101,8 +101,8 @@ for CLC_S in (:CLCCS, :CLCDS)
     end
 end
 
-# x' = Ax + c, x ∈ X, u ∈ U in the continuous case
-# x+ = Ax + c, x ∈ X, u ∈ U in the discrete case
+# x' = Ax + b, x ∈ X, u ∈ U in the continuous case
+# x+ = Ax + b, x ∈ X, u ∈ U in the discrete case
 for (CA_S, CLC_S) in ((:CACS, :CLCCS), (:CADS, :CLCDS))
     @eval begin
         function normalize(system::$CA_S{N, AN, VN, XT}) where {N, AN<:AbstractMatrix{N}, VN<:AbstractVector{N}, XT<:XNCF{N}}
@@ -114,6 +114,19 @@ for (CA_S, CLC_S) in ((:CACS, :CLCCS), (:CADS, :CLCDS))
     end
 end
 
+# x' = Ax + b in the continuous case
+# x+ = Ax + b in the discrete case
+for (A_S, CLC_S) in ((:ACS, :CLCCS), (:ADS, :CLCDS))
+    @eval begin
+        function normalize(system::$A_S{N, AN, VN}) where {N, AN<:AbstractMatrix{N}, VN<:AbstractVector{N}}
+            n = statedim(system)
+            X = Universe(n)
+            U = _wrap_inputs(system.b)
+            $CLC_S(system.A, I(n, N), X, U)
+        end
+    end
+end
+
 # x' = Ax + Bu + c, x ∈ X, u ∈ U in the continuous case
 # x+ = Ax + Bu + c, x ∈ X, u ∈ U in the discrete case
 for (CAC_S, CLC_S) in ((:CACCS, :CLCCS), (:CACDS, :CLCDS))
diff --git a/src/Utils/systems.jl b/src/Utils/systems.jl
index eca9bb62..c2edca60 100644
--- a/src/Utils/systems.jl
+++ b/src/Utils/systems.jl
@@ -10,6 +10,8 @@ const CLCS = ConstrainedLinearContinuousSystem
 const CLDS = ConstrainedLinearDiscreteSystem
 const CLCCS = ConstrainedLinearControlContinuousSystem
 const CLCDS = ConstrainedLinearControlDiscreteSystem
+const ACS = AffineContinuousSystem
+const ADS = AffineDiscreteSystem
 const CACCS = ConstrainedAffineControlContinuousSystem
 const CACDS = ConstrainedAffineControlDiscreteSystem
 const CACS = ConstrainedAffineContinuousSystem