Stability analysis and stabilization of systems presenting nested saturations

This paper addresses the problems of stability analysis and stabilization of systems presenting nested saturations. In the analysis problem the objective is the determination of estimates of the basin of attraction of the system. Considering the stabilization problem, the goal is to design a set of gains in order to enlarge the basin of attraction of the system. Based on the modelling of the closed-loop system as a linear system with dead-zone nested nonlinearities and the use of a modified sector condition, LMI stability conditions are formulated. Based on this condition, convex optimization problems are proposed to determine solution for both problems.