Design of Observer-Based Linear Robust Controllers

In this paper, we investigate the possibility of determining a linear robust control law when the full-state cannot be measured and observers are implemented to estimate the state. We focus on systems where the uncertainty satisfies the matching condition. The control law and the observer are designed using two Riccati equations. A preliminary result establishes that if scalar parameters are chosen so that a matrix inequality is satisfied, the closed loop system is stable for the uncertainty levels of interest. Our main result shows that if the transfer function of the nominal system (or a `squared-down´ form of it) does not have zeros in the right half plane, and there are at least as many sensors as there are actuators, the closed loop system can be stabilized by the approach used here regardless of the size of the uncertainty bounding Set.