ROBUST LINEAR CONTROLLERS USING OBSERVERS

In this note, 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. Our first result establishes that if certain scalar parameters are chosen so that a matrix inequality is satisfied, the closed-loop system is stable for the uncertainty levels of interest. Next, we show that if there are at least as many sensors as there are actuators and the transfer function of the nominal system (or a "squared-down" form of it) does not have zeros in the closed right-half plane, the closed-loop system can be stabilized by our technique, regardless of the size of the uncertainty bounding set.