diff --git a/crates/lyapunov/src/integrators/rk4.rs b/crates/lyapunov/src/integrators/rk4.rs
index 6f68680..1678a72 100644
--- a/crates/lyapunov/src/integrators/rk4.rs
+++ b/crates/lyapunov/src/integrators/rk4.rs
@@ -2,7 +2,7 @@ use crate::units::*;
 
 use crate::{
     integrators::traits::Accumulate,
-    traits::{Integrator, System, TimeDerivative},
+    traits::{Integrator, System, TimeDerivative, TimeInvariantSystem},
 };
 
 pub struct Rk4;
@@ -32,3 +32,35 @@ where
             .add_scaled(dt / 6.0, &k4)
     }
 }
+
+impl Rk4 {
+    pub fn step_ti<S, const N: usize, const M: usize>(
+        &self,
+        system: &S,
+        x: &S::State,
+        u: &S::Input,
+        dt: Time,
+    ) -> S::State
+    where
+        S: TimeInvariantSystem<N, M>,
+        S::State: Clone + TimeDerivative + Accumulate<<S::State as TimeDerivative>::Derivative>,
+    {
+        let half_dt = dt * 0.5;
+
+        let k1 = system.derivatives(x, u);
+
+        let x2 = x.add_scaled(half_dt, &k1);
+        let k2 = system.derivatives(&x2, u);
+
+        let x3 = x.add_scaled(half_dt, &k2);
+        let k3 = system.derivatives(&x3, u);
+
+        let x4 = x.add_scaled(dt, &k3);
+        let k4 = system.derivatives(&x4, u);
+
+        x.add_scaled(dt / 6.0, &k1)
+            .add_scaled(dt / 3.0, &k2)
+            .add_scaled(dt / 3.0, &k3)
+            .add_scaled(dt / 6.0, &k4)
+    }
+}
diff --git a/crates/lyapunov/src/lib.rs b/crates/lyapunov/src/lib.rs
index 572d9d6..a5954c5 100644
--- a/crates/lyapunov/src/lib.rs
+++ b/crates/lyapunov/src/lib.rs
@@ -18,4 +18,4 @@ pub use units::{BackEmfConstant, CurrentRate, FrictionCoefficient, TorqueConstan
 pub use controllers::linear_feedback::LinearFeedback;
 pub use integrators::rk4::Rk4;
 pub use systems::linear_system::LinearSystem;
-pub use traits::{Controller, Integrator, System, TimeDerivative};
+pub use traits::{Controller, Integrator, System, TimeDerivative, TimeInvariantSystem};
diff --git a/crates/lyapunov/src/systems/dc_motor.rs b/crates/lyapunov/src/systems/dc_motor.rs
index 5e71ff0..8ea0f30 100644
--- a/crates/lyapunov/src/systems/dc_motor.rs
+++ b/crates/lyapunov/src/systems/dc_motor.rs
@@ -2,7 +2,7 @@ use crate::units::*;
 
 use crate::inputs::{CurrentInput, VoltageInput};
 use crate::states::{CurrentRateState, CurrentState, OmegaAlphaState, ThetaOmegaState};
-use crate::traits::{Saturate, System, TimeDerivative};
+use crate::traits::{Saturate, TimeDerivative, TimeInvariantSystem};
 
 #[derive(Clone, Copy, Debug)]
 pub struct DCMotor {
@@ -110,13 +110,12 @@ impl DCMotor {
     }
 }
 
-impl System<1, 1> for DCMotor {
+impl TimeInvariantSystem<1, 1> for DCMotor {
     type State = CurrentState;
     type Input = VoltageInput;
 
     fn derivatives(
         &self,
-        _t: Time,
         x: &Self::State,
         u: &Self::Input,
     ) -> <Self::State as TimeDerivative>::Derivative {
@@ -160,13 +159,12 @@ impl DCMotorPosition {
     }
 }
 
-impl System<2, 1> for DCMotorPosition {
+impl TimeInvariantSystem<2, 1> for DCMotorPosition {
     type State = ThetaOmegaState;
     type Input = VoltageInput;
 
     fn derivatives(
         &self,
-        _t: Time,
         x: &Self::State,
         u: &Self::Input,
     ) -> <Self::State as TimeDerivative>::Derivative {
diff --git a/crates/lyapunov/src/systems/linear_system.rs b/crates/lyapunov/src/systems/linear_system.rs
index 5fe9410..55f0ace 100644
--- a/crates/lyapunov/src/systems/linear_system.rs
+++ b/crates/lyapunov/src/systems/linear_system.rs
@@ -1,6 +1,6 @@
 use crate::inputs::AccelerationInput;
 use crate::states::{PositionVelocityState, VelocityAccelerationState};
-use crate::traits::{System, TimeDerivative, VectorValue};
+use crate::traits::{TimeDerivative, TimeInvariantSystem, VectorValue};
 use crate::units::*;
 use nalgebra::{DMatrix, DVector, SMatrix, SVector};
 
@@ -28,13 +28,12 @@ impl<const N: usize, const M: usize> LinearSystem<N, M> {
     }
 }
 
-impl<const N: usize, const M: usize> System<N, M> for LinearSystem<N, M> {
+impl<const N: usize, const M: usize> TimeInvariantSystem<N, M> for LinearSystem<N, M> {
     type State = SVector<f64, N>;
     type Input = SVector<f64, M>;
 
     fn derivatives(
         &self,
-        _t: Time,
         x: &Self::State,
         u: &Self::Input,
     ) -> <Self::State as TimeDerivative>::Derivative {
@@ -85,13 +84,12 @@ impl DoubleIntegrator {
     }
 }
 
-impl System<2, 1> for DoubleIntegrator {
+impl TimeInvariantSystem<2, 1> for DoubleIntegrator {
     type State = PositionVelocityState;
     type Input = AccelerationInput;
 
     fn derivatives(
         &self,
-        _t: Time,
         x: &Self::State,
         u: &Self::Input,
     ) -> <Self::State as TimeDerivative>::Derivative {
diff --git a/crates/lyapunov/src/systems/pendulum.rs b/crates/lyapunov/src/systems/pendulum.rs
index d3d9bba..2519bf9 100644
--- a/crates/lyapunov/src/systems/pendulum.rs
+++ b/crates/lyapunov/src/systems/pendulum.rs
@@ -4,7 +4,7 @@ use crate::inputs::CurrentInput;
 use crate::states::{OmegaAlphaState, ThetaOmegaState};
 use crate::systems::LinearSystem;
 use crate::systems::dc_motor::DCMotor;
-use crate::traits::{Saturate, System, TimeDerivative};
+use crate::traits::{Saturate, TimeDerivative, TimeInvariantSystem};
 use nalgebra::{SMatrix, SVector};
 
 #[derive(Clone, Copy, Debug)]
@@ -63,13 +63,12 @@ impl Pendulum {
     }
 }
 
-impl System<2, 1> for Pendulum {
+impl TimeInvariantSystem<2, 1> for Pendulum {
     type State = ThetaOmegaState;
     type Input = CurrentInput;
 
     fn derivatives(
         &self,
-        _t: Time,
         x: &Self::State,
         u: &Self::Input,
     ) -> <Self::State as TimeDerivative>::Derivative {
diff --git a/crates/lyapunov/src/traits.rs b/crates/lyapunov/src/traits.rs
index d6b534e..3f34786 100644
--- a/crates/lyapunov/src/traits.rs
+++ b/crates/lyapunov/src/traits.rs
@@ -17,7 +17,6 @@ pub trait System<const N: usize, const M: usize> {
     type Input;
 
     // Evaluate the derivative vector x_dot at (t, x, u)
-    // TODO Create time-invariant system trait?
     fn derivatives(
         &self,
         t: Time,
@@ -26,6 +25,34 @@ pub trait System<const N: usize, const M: usize> {
     ) -> <Self::State as TimeDerivative>::Derivative;
 }
 
+pub trait TimeInvariantSystem<const N: usize, const M: usize> {
+    type State: TimeDerivative;
+    type Input;
+
+    fn derivatives(
+        &self,
+        x: &Self::State,
+        u: &Self::Input,
+    ) -> <Self::State as TimeDerivative>::Derivative;
+}
+
+impl<T, const N: usize, const M: usize> System<N, M> for T
+where
+    T: TimeInvariantSystem<N, M>,
+{
+    type State = T::State;
+    type Input = T::Input;
+
+    fn derivatives(
+        &self,
+        _t: Time,
+        x: &Self::State,
+        u: &Self::Input,
+    ) -> <Self::State as TimeDerivative>::Derivative {
+        self.derivatives(x, u)
+    }
+}
+
 // Computes the evolution of a system over (t, x, u)
 pub trait Integrator<S, const N: usize, const M: usize>
 where