Stability analysis of Lure systems under aperiodic sampled-data control

This article deals with the stability analysis of Lure type systems through aperiodic sampled-data control laws, where the nonlinearity is assumed to be both sector and slope restricted. The proposed method is based on the use of a new class of looped-functionals, which depends on the nonlinearity and its slope, and on a generalized Lure type function, that is quadratic on both the states and the nonlinearity and has a Lure-Postnikov integral term. On this basis, conditions in the form of linear matrix inequalities to certify global or regional asymptotic stability of the closed-loop system are obtained. These conditions are then used in optimization problems for computing the maximum intersampling interval or the maximum sector bounds for which the stability of the sampled-data closed-loop system is guaranteed. Numerical examples to illustrate the results are provided.