Delay-range-dependent stability criteria for Lur´e system with interval time-varying delay

In this paper, we investigate the problem of absolute stability and robust stability for a class of Lur´e systems with interval time-delay using Lyapunov-Krasovskii functional approach. By constructing a candidate Lyapunov-Krasovskii (LK) functional, delay-range-dependent stability criteria are developed for nominal and uncertain Lur´e systems in terms of linear matrix inequalities. For deriving robust stability conditions, time-varying norm-bounded uncertainties are considered in the system matrices. Conservatism in the proposed delay-dependent stability analysis is minimized through the use of a candidate LK functional, and tighter bounding conditions for dealing the cross-terms that emerge from the time-derivative of the functional. Finally, a numerical example is employed to validate the effectiveness of the proposed stability criteria.