| Three control design results based on worst-case analysis approach are presented in this dissertation. The first result is on robust adaptive control design for SISO linear systems with zero relative degree under noisy output measurements. The proposed adaptive controller asymptotically cancels out, at the output, the effect of exogenous sinusoidal disturbance inputs with unknown magnitude, phase, and frequency. The second result is on robust adaptive controller design for SISO linear systems with noisy output measurements and partly measured disturbances. The same results as those in [38] are achieved. In addition, when the relative degrees from the measured disturbances to the output are no less than that from the control input, the controllers designed achieve zero disturbance attenuation level with respect to the measured disturbance inputs. The asymptotic tracking objective is achieved even if the measured disturbance is only uniformly bounded, without requiring it to be of finite energy. The third result is on robust adaptive controller design for a special class of MIMO system, which is composed of two SISO linear subsystems under noisy output measurements, S1 and S2, sequentially interconnected with additional feedback. The closed-loop system admits a guaranteed disturbance attenuation level with respect to the exogenous disturbance inputs, where the ultimate attenuation lower bound for the achievable performance level is equal to the noise intensity in the measurement channel of S1. All these strong robustness properties are illustrated by numerical examples. |
