matplotlib.axes.Axes.bar does not support stacking out of the box. pandas.DataFrame.plot.bar does support stacking, but not ordered stacking. Here is an implementation of ordered stacking.

Ordered stacked matplotlib bar chart

import matplotlib.pyplot as plt
import pandas as pd
import numpy as np
a = pd.DataFrame({'a':[0.25, 0.5, 0.15, 0], 'b':[0.15, 0.25, 0.35, 0.15], 
                  'c':[0.50, 0.15, 0.5, 0.35], 'd':[0.35, 0.35, 0.25, 0.5],})
fig, ax = plt.subplots()
x = a.index
indexes = np.argsort(a.values).T
heights = np.sort(a.values).T
order = -1
bottoms = heights[::order].cumsum(axis=0)
bottoms = np.insert(bottoms, 0, np.zeros(len(bottoms[0])), axis=0)
mpp_colors = dict(zip(a.columns, plt.rcParams['axes.prop_cycle'].by_key()['color']))
for btms, (idxs, vals) in enumerate(list(zip(indexes, heights))[::order]):
    mps = np.take(np.array(a.columns), idxs)
    ax.bar(x, height=vals, bottom=bottoms[btms], color=[mpp_colors[m] for m in mps])
ax.set_ylim(bottom=0, top=2)
plt.legend((np.take(np.array(a.columns), np.argsort(a.values)[0]))[::order], loc='upper right')