Synthesis of output feedback controllers for a class of nonlinear parameter-varying discrete-time systems subject to actuators limitations

We present a methodology for computing output feedback control laws for a class of nonlinear systems subject to input saturations. This class of systems consists of a L´ure type nonlinear system with some time-varying parameters which are assumed to be real-time available. Based on some tools from the absolute stability theory, on a modified sector condition to take into account input saturation effects, and on the concept of contractive sets applied to a level set obtained from a particular parameter dependent Lyapunov function, an LMI framework is proposed to design dynamic output feedback compensators. Two local stabilization strategies are considered: (i) with saturation avoidance, and (ii) with saturating actuators. In both cases, convex optimization problems are proposed to compute the controllers matrices aiming at the maximization of the basin of attraction.