A hybrid approach to the stability analysis of sampled-data Lur’e systems

Abstract

This work deals with the stability analysis of Lur’e systems under sampled-data control, where the Lur’e nonlinearity is assumed to be both sector and slope restricted. The stability conditions are derived by using a hybrid system representation and a generalized Lur’e type timer-dependent Lyapunov function. Considering a polynomial timer-dependence, the stability conditions are cast in sum-of-squares optimization problems aiming at computing the largest range of sampling intervals or the largest sector bounds on the nonlinearity for which the origin of the closed-loop system is globally asymptotically stable.