ABSTRACT
This chapter aims to relax the requirement of the exponential stability of the nominal uncontrolled part of the system by making use of a version of the receding horizon control method. In a great part of the literature, continuous systems are considered. Stability issues for discrete time uncertain systems without any control constraint have been discussed. The chapter provides a neighbourhood of the origin, in which the controller can be given as the sum of two terms: one of them is a linear feedback for exponential stabilization of the nominal part of the system, the other is a nonlinear feedback for counteracting the uncertainty. It presents a method of stabilization of nonlinear, discrete-time uncertain systems in which the uncertainties are modeled deterministically rather than stochastically. The control has been subject to the hard constraint with a prespecified constant. The nonlinear feedback has been constructed by using Lyapunov stability theory.
