Adaptive control for tracking and disturbance attenuation for SISO linear systems with repeated noisy measurements

We address the worst-case adaptive controller design for single-input linear systems with repeated noisy measurements of a particular linear combination of the state variables to achieve asymptotic tracking and disturbance attenuation. Using the design paradigm outlined in [1], we obtained a class of single-input multiple-output adaptive controllers in closed-form with strong robustness properties. It is shown that the closed-loop system is totally stable with respect to the disturbance and the initial condition. Furthermore, when the exogenous disturbance has bounded energy and is uniformly bounded, the closed-loop system achieves asymptotic tracking of the reference trajectory. This design is further compared with certain single-input single-output design for trade-offs.