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

Abstract

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.