Stability of nonlinear differential delay systems

Sufficient conditions for the robust stability (independent of the delay) of linear differential delay systems have been obtained based on the Lyapunov–Krasovskii theory. These sufficient conditions are `nice' in the sense that they involve the existence of a triple of positive definite matrices satisfying a certain Riccati equation [21, 22], and therefore `algebrize' robust stability results. These robust stability results are here extended to local stability conditions for differential delay systems with nonlinear perturbations. For sector bounded nonlinearities global results for robust stability are also obtained, based on the Lur'e–Postnikov theory.