Delay-Dependent Absolute Stability ofUncertain Lur′e Systems with Time-Delays^1）

This paper is concerned with delay dependent absolute stability for a class of uncertain Lur′e systems with multiple time-delays. By using a descriptor model transformation of the sys-tem and by applying a recent result on bounding of cross products of vectors, a new type of Lya-punov-Krasovskii functional is constructed. Based on the new functional, delay-dependent suffi-cient conditions for absolute stability are derived in terms of linear matrix inequalities. These con-ditions do not require any parameter tuning, and can be solved numerically using the software LMI Lab. A numerical example is presented which shows that the proposed method can substantiallyimprove the delay bound for absolute stability of Lur′e system with time-delays, compared to theexisting ones.