Stable adaptive controller design. II - Proof of stability

The paper presents a proof of stability of model reference adaptive control systems using direct control. The structure of the adaptive system is similar to that considered by Monopoli (Oct. 1974) and Narendra and Valavani (Aug. 1978) but contains an additional feedback term which ensures that the time derivative of the parameter error vector belongs to the L(2) space. The output of the plant is shown to be bounded by expressing the plant feedback loop as an exponentially stable system with a time-varying gain in the feedback path.