Observer-based robust stabilization for a class of uncertain delay system

The observer-based robust stabilization of uncertain system with unknown constant state delay in an interval is studied. A sufficient condition is given for the existence of the state observer and observer-based robust controllers for such uncertain system. The design method of the state observer and observer-based robust controller is presented by solving two linear matrix inequalities (LMIs). Because the designed observer is the observer with delay, the conservation is reduced in the conclusion. At last, an illustrative numerical example is presented, which shows the effectiveness of the proposed method.