Stability of discrete model reference adaptive control — revisited

We demonstrate that the model reference adaptive controller is robust with respect to small model/plant mismatch. The sign and a lower bound on the high frequency gain are known and the control parameters are constrained to belong to a compact set which contains the parameters of a stabilizing controller. Data normalization and deadzones do not play a role in the analysis. A constructive proof is used to develop bounds for the allowable gain of the model mismatch. When the algorithm state is far from equilibrium the signals are measured by a decaying exponential. The rate of convergence is estimated. An expression which can be used to calculate the size of an overbounding set is developed. Its size scales uniformly with respect to the external disturbances, the inverse of the adaptive gain and the reference. The ideal case is obtained as these tend to zero. This result holds true even when there is a model mismatch.