Further enhancement of delay-range-dependent stability criteria for systems with time-varying delays

Recently, as a way of reducing conservatism in the stability analysis of time-delayed systems, some triple integral terms in the Lyapunov-Krasovskii functional have been introduced in the literature. However, they could not be manipulated properly in the derivation of LMI conditions owing to the emergence of squared parameters, which cannot be handled directly by [8]´s relaxation method. This paper proposes an efficient way of manipulating the triple integral terms in the Lyapunov-Krasovskii functional. There are produced two combinations of delay-dependent functions, one with positive functions weighted by mutually inverse parameters and the other with negative functions weighted by inverses of convex parameters. The former combination is transformed to a condition that is linear in delay, and the latter is handled efficiently by [7]´s relaxation method. Some numerical examples are given to demonstrate the effectiveness of the proposed method.