This article addresses an invariant sets approach for Youla-Kuc. era parameter synthesis using linear matrix inequality (LMI) techniques. Given a linear discrete-time observer-based system affected by bounded disturbances and constraints, the proposed technique furnishes the best Youla parameter in terms of finding an invariant ellipsoidal set satisfying the constraints and having the maximal ellipsoidal projection on the state space. Compared with the results obtained for an observer-based design, the synthesis of a Youla parameter provides a larger ellipsoidal projection and an improved sensitivity function. The price to pay for these achievements in terms of robustness is usually a slow closed-loop performance with degraded complementary sensitivity function. In order to obtain a compromise between robustness and performance two methods are proposed: the first method imposes a new bound on the Lyapunov function decreasing speed and the second refers to the pole placement concept. The aforementioned approaches are finally validated in simulation considering position control of an induction motor.