diff --git a/ampyc/plotting/plot_u.py b/ampyc/plotting/plot_u.py
index 2af695b..63b0f7e 100644
--- a/ampyc/plotting/plot_u.py
+++ b/ampyc/plotting/plot_u.py
@@ -12,6 +12,7 @@
 
 from ampyc.typing import Params
 from ampyc.utils import Polytope
+from .plot_x import plot_constraints
 
 def plot_u(fig_number: int,
            u: np.ndarray,
@@ -49,8 +50,7 @@ def plot_u(fig_number: int,
 
     ax.plot(u, color=params.color, alpha=params.alpha, linewidth=params.linewidth, label=label)
     if U is not None:
-        ax.axline((-1, U.vertices.max()), slope=0, color='k', linewidth=2)
-        ax.axline((-1, U.vertices.min()), slope=0, color='k', linewidth=2)
+        plot_constraints(fig, U)
     ax.set_xlabel('time')
     ax.set_ylabel(axes_labels[0])
     ax.set_xlim([0, num_steps])
diff --git a/ampyc/plotting/plot_x.py b/ampyc/plotting/plot_x.py
index d5e60f9..27625e0 100644
--- a/ampyc/plotting/plot_x.py
+++ b/ampyc/plotting/plot_x.py
@@ -9,10 +9,24 @@
 
 import numpy as np
 import matplotlib.pyplot as plt
+from matplotlib.figure import Figure
 
 from ampyc.typing import Params
 from ampyc.utils import Polytope
 
+
+def plot_constraints(
+    fig: Figure,
+    X: Polytope,
+):
+    mins, maxes = X.bounding_box
+    for i, ax in enumerate(fig.axes):
+        if np.isfinite(mins[i, 0]):
+            ax.axline((-1, mins[i, 0]), slope=0, color='k', linewidth=2)
+        if np.isfinite(maxes[i, 0]):
+            ax.axline((-1, maxes[i, 0]), slope=0, color='k', linewidth=2)
+
+
 def plot_x_state_time(
         fig_number: int,
         x: np.ndarray,
@@ -21,15 +35,15 @@ def plot_x_state_time(
         label: str | None = None,
         legend_loc: str = 'upper right',
         title: str | None = None,
-        axes_labels: list[str] = ['x_1', 'x_2'],
+        axes_labels: list[str] | None = None,
         ) -> None:
     '''
     Plots the state trajectory x over time, including the state constraint set X.
-    This function assumes a 2D state space (n=2) and plots the two state variables against time.
+    This function plots the state variables against time.
 
     Args:
         fig_number (int): The figure number to use for the plot. This allows multiple plots in the same figure.
-        x (np.ndarray): The state trajectory, shape (N, n=2, T), where N is the number of time steps,
+        x (np.ndarray): The state trajectory, shape (N, n, T), where N is the number of time steps,
                         n is the state dimension, and T is the number of trajectories.
         X (Polytope | None): The state constraint set.
         params (Params): Parameters for plotting, e.g., color, alpha, and linewidth.
@@ -39,23 +53,34 @@ def plot_x_state_time(
         axes_labels (list[str]): Labels for the x and y axes.
     '''
 
+    n = x.shape[1]
+    if axes_labels is None:
+        axes_labels = [f'x_{{{i+1}}}' for i in range(n)]
+
     # check if the figure number is already open
     if plt.fignum_exists(fig_number):
         fig = plt.figure(fig_number)
-        ax1 = fig.axes[0]
-        ax2 = fig.axes[1]
+        axes = fig.axes
     else:
-        fig, (ax1, ax2) = plt.subplots(2,1, num=fig_number, sharex=True)
+        fig, axes = plt.subplots(n,1, num=fig_number, sharex=True)
 
     num_steps = x.shape[0]
 
-    ax1.plot(x[:,0], color=params.color, alpha=params.alpha, linewidth=params.linewidth, label=label)
+    for i, ax in enumerate(axes):
+        kwargs = {}
+        if i == 0:
+            kwargs['label'] = label
+        ax.plot(x[:,i], color=params.color, alpha=params.alpha, linewidth=params.linewidth, **kwargs)
+        if i == n - 1:
+            ax.set_xlabel('time')
+        ax.set_ylabel(axes_labels[i])
+        ax.set_xlim([0, num_steps])
+        ax.grid(visible=True)
+
     if X is not None:
-        ax1.axline((-1, X.vertices[:,0].max()), slope=0, color='k', linewidth=2)
-        ax1.axline((-1, X.vertices[:,0].min()), slope=0, color='k', linewidth=2)
-    ax1.set_ylabel(axes_labels[0])
-    ax1.set_xlim([0, num_steps])
-    ax1.grid(visible=True)
+        plot_constraints(fig, X)
+
+    ax1 = axes[0]
     if title is not None:
         ax1.set_title(title)
 
@@ -64,15 +89,6 @@ def plot_x_state_time(
         handles, labels = ax1.get_legend_handles_labels()
         by_label = dict(zip(labels, handles))
         ax1.legend(by_label.values(), by_label.keys(), loc=legend_loc)
-    
-    ax2.plot(x[:,1], color=params.color, alpha=params.alpha, linewidth=params.linewidth)
-    if X is not None:
-        ax2.axline((-1, X.vertices[:,1].max()), slope=0, color='k', linewidth=2)
-        ax2.axline((-1, X.vertices[:,1].min()), slope=0, color='k', linewidth=2)
-    ax2.set_xlabel('time')
-    ax2.set_ylabel(axes_labels[1])
-    ax2.set_xlim([0, num_steps])
-    ax2.grid(visible=True)
 
     fig.tight_layout()
 
diff --git a/notebooks/tutorial.ipynb b/notebooks/tutorial.ipynb
index 4d06d41..216a009 100644
--- a/notebooks/tutorial.ipynb
+++ b/notebooks/tutorial.ipynb
@@ -1518,7 +1518,7 @@
    "source": [
     "For convenience, the AMPyC package also contains basic plotting functions. Here we use a state-state plot and an input-time plot to visualize the trajectories produced by the MPC.\n",
     "\n",
-    "**Note:** All plotting functions shipped with the AMPyC package assume a 2D state and a 1D input."
+    "**Note:** Most plotting functions shipped with the AMPyC package assume a 2D state and a 1D input."
    ]
   },
   {