  Ensuring nominal asymptotic stability of the Non-linear Model Predictive
Control (NMPC) controller is not trivial. Stabilizing ingredients such as
terminal penalty term and terminal region are crucial in establishing the
asymptotic stability. Approaches available in the literature provide limited
degrees of freedom for the characterization of the terminal region for the
discrete time Quasi Infinite Horizon NMPC (QIH-NMPC) formulation. Current work
presents alternate approaches namely arbitrary controller based approach and
LQR based approach, which provide large degrees of freedom for enlarging the
terminal region. Both the approaches are scalable to system of any state and
input dimension. Approach from the literature provides a scalar whereas
proposed approaches provide a linear controller and two additive matrices as
tuning parameters for shaping of the terminal region. Proposed approaches
involve solving modified Lyapunov equations to compute terminal penalty term,
followed by explicit characterization of the terminal region. Efficacy of the
proposed approaches is demonstrated using benchmark two state system. Terminal
region obtained using the arbitrary controller based approach and LQR based
approach are approximately 10.4723 and 9.5055 times larger by area measure when
compared to the largest terminal region obtained using the approach from the
literature.
