On designing stochastic sampled-data controller for master–slave synchronization of chaotic Lur’e system via a novel integral inequality

• Less conservative synchronization conditions are obtained by using a novel approach.
• Based on the extended Wirtinger inequality, a newly time-dependent Lyapunov–Krasovskii functional is constructed by introducing two independent random variable parameters.
• By using a novel free-matrix-based integral inequality, a desired estimator gain can be achieved.
• Numerical simulation examples are given to illustrate the effectiveness and superiorities of the proposed method.

This study investigates the problem of designing stochastic sampled-data controller for master–slave synchronization of chaotic Lur’e systems (CLSs) via a novel approach. Specially, first, we assume that the occurrence probabilities of the sampling intervals are fixed constants and satisfy a Bernoulli distribution. In order to take full advantage of the sawtooth structure characteristics of the sampling input delay, we construct a newly augmented Lyapunov–Krasovskii functional (LKF) based on the extended Wirtinger inequality. Second, by using a novel free-matrix-based integral inequality (FMBII) including well-known integral inequalities as special cases, an exponentially mean-square synchronization criterion is proposed for analyzing the corresponding synchronization error system. Third, the desired estimator gain can be designed in terms of the solution to linear matrix inequalities (LMIs) which can be solved effectively by using available software. Finally, three numerical simulation examples of Chua’s circuit and neural network are given to illustrate the effectiveness and superiorities of the proposed method.