Robust linear controllers using observers

The possibility of determining a linear robust control law when the full state cannot be measured and observers are implemented to estimate the state is considered. The focus is on systems where the uncertainty satisfies the matching condition. The control law and the observer are designed using two Riccati equations. The 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. It is then shown 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 the technique, regardless of the size of the uncertainty bounding set