Robust Observer-Based Stabilization and Tracking of Uncertain Linear Systems with L2-gain Performance: Application to DC motors

New linear-matrix-inequality-based results on observer-based controller design for stabilization and trajectory tracking of uncertain linear systems subject to polytopic uncertainties and exogenous disturbances are presented. The observer dynamics along with the stabilizing feedback are designed using convex optimization technique with a prescribed L-2-gain performance. The solution of the original non-convex optimization problem is transformed into the solutions of a set of linear matrix inequalities (LMIs) without introducing equality constraints or iterative search. The effectiveness of the proposed results is demonstrated by position control of a DC motor under parametric uncertainties and load torque disturbance.