Stability of feedback error learning method with time delay

Feedback error learning method was recently proposed by Kawato et al. [A heirarchical neural-network model for control and learning of voluntary movements, Biol. Cybernet. 57 (1987) 169–185.] as a possible architecture of brain motor control which is supported by experimental results in neurophysiology. In this paper, we analyze it as a two-degree-of-freedom adaptive control for general time invariant linear plant with adaptive controller in the feedforward path. A time delay is allowed in the feedback loop as in the neuronal pathways of motor control. We derive stability condition of the feedback error learning method based on the strict positiveness of the closed loop system. The control performance of the feedback error learning method as a design strategy of adaptive control has been demonstrated by simulation results.