This paper presents some results on the stabilization by a parameter dependent control law of a class of nonlinear discrete-time systems with some time-varying parameters and 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, LMI stabilization conditions are proposed, which can be cast into convex programming problems to synthesizing the gain matrices that allows to construct the parameter dependent control law. The presented numerical example shows some performance issues and compares the proposed parameter dependent control law with a fixed parameters one.
Nonlinear systems; Saturations; Parameter dependent Lyapunov functions; Parameter dependent control; LMIs; Robustness
