Stability analysis of Lur'e systems with additive delay components via a relaxed matrix inequality

This paper is concerned with the stability analysis of Lur'e systems with sector-bounded nonlinearity and two additive time-varying delay components. In order to accurately understand the effect of time delays on the system stability, the extended matrix inequality for estimating the derivative of the Lyapunov-Krasovskii functionals (LKFs) is employed to achieve the conservatism reduction of stability criteria. It reduces estimation gap of the popular reciprocally convex combination lemma (RCCL). Combining the extended matrix inequality and two types of LKFs lead to several stability criteria, which are less conservative than the RCCL-based criteria under the same LKFs. Finally, the advantages of the proposed criteria are demonstrated through two examples.