Can a pendulum stabilizer for airplanes really work? Can a pendulum really stabilize a plane for both roll and pitch?

I have read about various experiments (the one in the picture being just a simple case) but I still do not find an example of plane that was stabilised beyond any doubt with the help of a pendulum.

As a note:
If the suspension point of a pendulum is at rest or moves at constant speed then after some oscilations the bob will end up by hanging vertically. However this is not the case when the suspension point has an accelerated movement. 


Source: Popular Science, December 1939

UPDATE

I have found a description (see the attached image) of a Wright stabilizer that was used successfully!! before February 1914. The roll was controlled by a pendulum (letter A in the picture) that swung along the main wings. At one point the article states that the device gave good results being tested daily for long intervals of time.

Another more recent text says that demonstrations were made before the Aero Club judges on December 31, 1913.


  In the fall of 1913, Orville installed the stabilizer on a special
  Wright Model E airplane that utilized a single pusher propeller. He
  kept the details of the stabilizer secret even from the Wright
  Company. He purposely waited until the last day of the year to fly for
  the prize.
  
  He invited the Aero Club’s judges to Huffman Prairie to see a
  demonstration of his new device on a cold snowy day, December 31st.
  
  He turned up his coat collar, put on a pair of goggles and took off.
  He made a total of 17 flights.
  
  His most spectacular flight consisted of 7 full circles of the field
  with both hands held in the air. The automatic stabilizer kept the
  same angle of bank and almost the same altitude. He wowed the judges
  and was awarded the prize on February 5, 1914.


Source: Wrights Develops Automatic Stabilizer

How is it possible?


Source: The Wright Automatic Stabilizer, L'Aerophile, February 1, 1914
As you noted, a pendulum can only "measure" pitch and roll angles when the pivot point is not accelerating.  Except, of course, if the length of the pendulum is the same as the Earth's radius — in which case we have a Schuler Pendulum.

Ed Carsten's pendulum stabilizer attempts to use the same principle as an autopilot measuring roll and pitch angles, and then generating elevator and aileron commands to level the aircraft. But this cannot work when using a pendulum of practical length since the roll and pitch angle "measurements" are in fact combinations of attitude angles and horizontal accelerations.