Stability criteria for delay systems with sector-bounded nonlinearities

The present note is devoted to the study of stability of delay systems with nonlinearities subject to sector conditions. We construct quadratic candidate Lyapunov-Krasovskii functional for various such systems, whose decreasingness along trajectories is expressed in terms of Linear Matrix Inequalities. We then show that the feasibility of the latter implies some frequency domain conditions, which may be seen as delay-independent versions of the circle criterion and the Popov criterion.