Stability analysis of a rapidly adapting control system

A method is given for stability analysis of a rapidly adapting model-reference system. The instantaneous value of the difference between model output and system output is used to adjust system gain. With proper compensating circuits in the adaptive controller, an error in plant gain is corrected in a time interval which is much less than the rise time of the system. The system performs equally well with square-wave, triangular, or sinusoidal inputs.