Robustness studies in adaptive control

It has been shown that several similar Model Reference Adaptive Controllers (MRAC's) are globally stable under certain restrictive assumptions, including the assumption that the order and relative degree of the plant are exactly known, and that no disturbances are present. Under certain 'sufficiently rich' excitation conditions, the origin is globally asymptotically stable for the adaptive controller parameter error. The time-evolution of the parameter error vector represents the key factor to the stability of the adaptive controller. This time-evolution is described by a complicated set of time-varying nonlinear differential equations. The present investigation is concerned with an approximate analysis technique for studying the long term trends of the parameter error vector trajectory for an adaptive controller under periodic excitation.