A novel equivalent reciprocal convex combination technique to sampled‐data master–slave synchronization for chaotic Lur'e systems with time‐varying delays

Abstract

AbstractFor a class of master–slave (M‐S) systems in chaotic Lur'e systems with time‐varying delays, a sampled‐data synchronization controller is designed, and a new synchronization stability condition is proposed in the form of linear matrix inequality. A novel Lyapunov‐Krasovskii functional (LKF) is constructed by using the looped‐functional method, and the positive definiteness condition of LKF including sampled‐data parts is exchanged with a looping condition by constructing a functional, which should be equal at adjacent sampling times. The M‐S synchronization condition is obtained utilizing the equivalent reciprocal convex combination approach combined with Bessel‐Legendre integral inequality to estimate the LKF derivative. Different from previous methods, due to fully utilizing both nonlinearity and state information at the sampling time via the integral of error systems from the sampling time to current one, the M‐S synchronization condition is less conservative, and obtained sampled‐data controller possesses a longer sampling period. Finally, two numerical examples verify the superiority and validity of the approach.