Reduced-order adaptive controller design for disturbance attenuation and asymptotic tracking for SISO linear systems with noisy output measurements

We study the reduced-order adaptive control design for SISO linear systems under noisy output measurements, as compared to the full-order adaptive control proposed in Z. Pan and T. Basar (July 2000). We make the same assumption as Z. Pan and T. Basar and follow the same design paradigm, where we simplify the dynamic order of the controllers by using a slightly modified design at a particular step of the control design. The dynamic order of the controllers obtained in this paper is n - 1 or n - 2 less than those presented in Z. Pan and T. Basar (July 2000), depending on the eigen-structure of a particular feedback matrix. We prove rigorously that reduced-order controllers admit the same robustness properties as those of Z. Pan and T. Basar. The order reduction simplifies the controller structure enormously without any sacrifice in performance. A numerical example is included in the paper, which demonstrates the improved performance resulting from the order reduction, even though there is no theory justifying the improvement.