This doctoral thesis deals with the control of nonlinear systems using generalized predictive controllers (GPCs) in state space. First a revision of designing methodology of the GPC in input/ouput (I/O) version is done. Departing from this revision a CARIMA model  in space of state for the GPC is proposed. This GPC in state space requires a lower amount of storing information, a lower computation time and has a easier formulation than I/O version. For the estimation of the  CARIMA model states it is proposed a full rank observer designed by pole placement, becoming established an important result: the  observer poles are equal to the roots of filter polynomials used in the  I/O formulation. After, the controllability and observability of CARIMA model are examined, taking place to the conclusion that under smooth conditions this model is a minimal realization, which supposes that prediction is based in a model with the minimal possible order.

After this, it is proposed a methodology of analysis and stable design of GPC in state space using the cost index as Lyapunov function, and when there are constraints the invariant set theory is applied to GPC.


Straightaway, a designing robust methodology is presented for the GPC based on linear inequalities matriciales (LMIs) and genetic algorithms. In short, the case of systems with fixed and time varying uncertainty with linear fractional dependence is analyzed, one of the most complex and general dependence used in the literature examined.

Finally, the GPC-LPV controller is presented as a extension of the GPC in state space. This controller is time varying (possibly nonlinear) having a linear fraction dependence with respect to signal measurements (usually output signals). His design is applicable to nonlinear systems whose dynamic models can be included inside of a linear time varying system using linear differential inclusion techniques. Its design is based on  bilinear matrix inequalities (BMIs), a generalization of LMIs.