Analysis of aperiodic sampled data Lur'e Systems using integral quadratic constraints

This paper considers the stability analysis of a class of sampled data Lur'e systems with possibly aperiodic sampling times. The analysis conditions are formulated in an IQC framework where i) the nonlinear component, as usual, is modelled using sector and slope restrictions which have well-known integral quadratic constraints associated with them; and ii) the sample-and-hold operator is represented, after loop transformations as an operator which satisfies certain other integral quadratic constraints. The arising analysis conditions can then be expressed as a frequency domain condition and a time domain constraint. Under various assumptions these can be transformed into linear matrix inequality conditions. Quite logically, when the bound on the sample interval tends to zero, the continuous time stability conditions for Lur'e systems are recovered.