Lyapunov-stable discrete-time model reference adaptive control

Discrete-time model reference adaptive control (MRAC) has been studied extensively. Although the framework of the analyses is very general, the results obtained are restricted to boundedness and convergence and the important question of Lyapunov stability is not addressed. Lyapunov functions are an important tool for understanding and quantifying transient response, robustness and disturbance rejection, and thus merit attention. In this paper we investigate the use of a logarithmic Lyapunov function to establish Lyapunov stability of MRAC in the deterministic setting. A complete Lyapunov proof is given for stability and convergence. The results extend the approach of R. Johansson, 1989, to include Lyapunov stability for MRAC when the normalized projection algorithm is used for parameter identification.