Youla-Kučera parameter synthesis using invariant sets techniques

This paper presents a new methodology for Youla-Kučera parameter synthesis using invariant sets techniques. For a linear discrete-time system affected by perturbations and constraints and with the state derived by means of an observer, the proposed method gives the best Youla parameter in terms of finding the maximal invariant ellipsoid satisfying the constraints. As a result of this technique that combines the advantages of the Youla parameter and the invariant set, a larger maximal ellipsoid is derived together with an improved sensitivity function compared to the ones obtained for the system with observer only. In order to improve also performances, considering complementary sensitivity function and transient response toward output disturbances, a new bound is imposed to the Lyapunov function. This approach is finally validated in simulation considering position control of an induction motor.