Delay-distribution-dependent Robust Stability Analysis of Uncertain Lurie Systems with Time-varying Delay

In this paper, the problem of robust absolute stability of Lurie system with probabilistic time-varying delay and norm-bounded parametric uncertainty is considered. The time delay variation range is divided into two subintervals. By considering the probability distribution of the time-varying delay between the two subintervals and the knowledge of the delay variation range, a novel linear matrix inequalities (LMIs) based stability condition is derived by defining a Lyapunov Krasovskii functional. It is illustrated with the help of numerical examples that the derived stability criteria can lead to less conservative results as compared to the results obtained by the traditional method of using the delay variation range information only.