Observers for stabilization of systems with matched uncertainty

Quadratic stabilizability and its connections to disturbance attenuation have been studied by various researchers. For example, controllers that stabilize the system while providing certain disturbance attenuation have been discussed. In the previous work, it was found that the uncertainty does not necessarily meet any matching conditions. As a result, the existence of a suitable control law depends on the satisfaction of a variety of sufficient conditions. The authors show that, when the uncertainty meets the matching conditions, the existence of suitable observer-based control laws can be guaranteed if the nominal system satisfies minimum-phase and invertibility conditions. Furthermore, this holds regardless of the size of the uncertainty (in the system matrix) and for any desired disturbance attenuation. Results presented concern uncertainty in either the input or the output matrices (but not both simultaneously)