STABILITY AND STABILIZATION OF A CLASS OF UNCERTAIN NONLINEAR DISCRETE-TIME SYSTEMS WITH SATURATING ACTUATORS

Abstract

This paper presents some results on stability and stabilization of a class of uncertain nonlinear discrete-time systems under control saturations. The studied control law consists of the feedback of both the states and of the nonlinearity present in the dynamics of the controlled system. Saturations are taken into account by modeling the nonlinear saturated system through a deadzone nonlinearity satisfying a modified sector condition. Thus, as for precisely known systems, LMI stability and stabilization conditions are proposed, which can be cast into convex programming problems. Some relations of the proposed results with the poly-quadratic stability concept are included.