Robust stability and performance of uncertain Lurie systems with state delays

In this paper, we consider the problem of persistent bounded disturbance rejection for uncertain Lurie systems with delay. We mainly focus on the problems of absolute stability (delay-independent stability and delay-dependent stability) and performance of bounded disturbance rejection using the Lyapunov-Krasovskii function method. In the two cases, we give sufficient conditions for guaranteeing simultaneously absolute stability and achieving certain performance of bounded disturbance rejection in terms of a linear matrix inequality (LMI). For the delay-dependent case, an estimate of the maximum admissible delay bound is established in terms of a generalized eigenvalue problem that can be solved numerically with the efficient LMI toolbox. Similarly, we study the corresponding problem for Lurie delay systems with uncertainties. Finally, two numerical examples are worked out to illustrate the effectiveness of the proposed results.