The report gives separate necessary and sufficient conditions in terms of the system and cost matrices for the attainment of a guaranteed disturbance attenuation ratio involving the estimate error for the continuous portion of the state. Furthermore, the report demonstrates that a guaranteed disturbance attenuation ratio cannot be achieved when a cost on the switching portion of the state is included, since an arbitrarily small measurement noise term can always be chosen so that one subsystem completely mimics the behavior of another subsystem. When there is no cost on the hybrid portion of the state, the report demonstrates that under a mild assumption, a finite guaranteed disturbance attenuation ratio can be achieved. My thesis research is concerned with robust identification of dynamical systems with parametric uncertainty when only a noisy full-state measurement is available. The systems considered are linear in the parameter, but otherwise generally nonlinear.
More detail appears in the reports below, which appear essentially in reverse chronological order.
I study these candidate algorithms by applying them in simulation to the longitudinal flight dynamics of the iced NASA Twin Otter. Simulations are performed for increasing levels of measurement noise, and the disturbance attenuation level gamma is estimated numerically for each case. In particular, I am interested in the behavior of the gamma estimate as the noise amplitude is increased.