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The Lyapunov–Krasovskii functional (LKF) method is widely used to derive-gain analysis criteria of delay systems. Nevertheless, how to improve the method for obtaining less conservative-gain analysis criteria is still an open problem. In this paper, an improved-gain analysis method called a delay-mode-based Lyapunov–Krasovskii functional (DMBLKF) method is proposed to replace the LKF method. This is achieved by weakening the condition that a LKF is required for a system with a delay varying in a delay interval. With the help of the DMBLKF method, new-gain analysis criteria of delayed neural networks are obtained and a numerical example is given to show that the DMBLKF method is more effective than the LKF method.

An improved -gain analysis method of nonlinear delay systems and its application to delayed neural networks