Absolute stability of uncertain discrete Lur'e systems and maximum admissible perturbed bounds

The robust absolute stability problem for norm uncertain and structured uncertain discrete Lur'e systems is considered in this paper by using Lyapunov function method. A sufficient condition of absolute stability for discrete Lur'e systems is established in terms of linear matrix inequalities (LMIs) or the equivalent frequency-domain condition. We compare the result with the Popov-like criterion (Tsypkin criterion) and extended strictly positive real (ESPR) lemma. Furthermore, sufficient conditions on absolute stability for discrete Lur'e systems with norm and structured uncertainties are also presented based on linear matrix inequalities. Estimates of the maximum bounds of all admissible perturbations are given by generalized eigenvalue problems. Finally, several numerical examples are worked out to illustrate the efficiency of the main results.