Further Improvements on Delay-Dependent Absolute Stability of Delayed Systems with Sector-bounded Nonlinearity

This note deals with the absolute stability of Lur´e control systems with time-varying delay. An augmented Lyapunov functional is introduced to establish some new stability criteria. First, for the nominal system, we develop some new stability conditions, by considering the additional useful terms and introducing some free-weighting matrices. In the proof of our results, we introduce some useful lemmas which have shown better effectiveness. Then, these new criteria are extended to the robust stability for uncertain systems with norm-bounded or polytopic-type uncertainties. The time-invariant and rate-independent delay criteria are obtained as some additional corollaries. Numerical examples show that the results obtained in this note improve the estimation of the stability limit over the existing ones.