Multivariable GPC and Kleinman´s controller: stability and equivalence

This paper shows how multivariable generalized predictive controller (MGPC) can be related to Kleinman´s controller. Basically, if these two controllers coincide, then stability of Kleinman´s controller means stability of MGPC. Additionally, the equivalence between these two controllers helps us to recognize the relationship between the original formulations of MPC and MPC with terminal equality constraint. For these purposes, Kleinman´s controller is also extended and the Riccati iteration formula is modified.