Application of polytopic separation techniques to nonlinear observer design

Output feedback control of nonlinear systems is an important open research topic which attracts attention for both its theoretical interest and its practical applications. This thesis relies on the theory developed by Maggiore and Passino in [27] towards a separation principle for nonlinear systems. That work crucially relies on the existence and construction of a set P, enjoying special properties, separating two non-convex sets. The class of sets P we choose to work with is that of polytopes. In this thesis we develop two algorithms to accomplish the task of separating two non-convex sets. The first algorithm relies on semi-infinite programming. The second algorithm relies on orthogonal projection and outer polytopic approximation. Both algorithms are first tested on basic examples and later used to design nonlinear observers for the Moore-Greitzer three-state model of surge and stall in jet engine compressors.