On employment of semidefinite functions in stability of delayed equations ✩

Four new stability theorems for nonautonomous delayed equations are established by the Lyapunov–Razumikhin approach with functions and its derivatives semidefinite. To do this, assume the collection of right-hand side translations in time has limit points which govern limiting equations. A corollary, which relates global asymptotic stability for the equation to that for limiting equations, and an illustrative example are given to show the applications of the established theorems.  2003 Elsevier Science (USA). All rights reserved