Polyhedral estimates of the region of attraction of the origin of linear systems under aperiodic sampling and input saturation

Abstract

This work addresses the stability analysis of linear aperiodic sampled-data systems under saturating inputs. A method to generate an increasing sequence of polyhedral estimates of the region of attraction of the origin of the closed-loop system is proposed. An impulsive system representation, given by a linear flow and a nonlinear jump dynamics due to the saturation term, is employed. From this representation, a convenient partition of the admissible interval for the intersampling time and an appropriate model of the saturation term, the computation of polyhedral contractive sets is carried out considering a convex embedding of the behavior of the system at the sampling instants. It is then shown that the computed polyhedra are included in the region of attraction of the continuous-time plant driven by the sampled-data control. A numerical example validates the theoretical developments and compares the method presented in this work with other approaches from the literature.