Application of quadratic Lyapunov functions to investigation of stability of systems with delay

The particular attention when studying delay systems is payed to such important systems property as its stability. When studying ordinary differential systems stability by Lyapunov functions method quadratic Lyapunov functions are widely used. This paper is devoted to usage as Lyapunov function for system with delay some quadratic Lyapunov functions constructed for ordinary differential system with limitation over its first derivative due to this system. The conditions of possibility of use of such quadratic functions as Lyapunov functions for delay system are presented.