<italic>H_&#x221E;</italic> Synchronization for Chaotic Lur&#x2019;e System With Uncertainty Based on Memory-Based Sampled-Data Control

Abstract

In this paper, the synchronization issue of chaotic Lur’e system (CLs) is investigated under the coupling memory sampled-data controller (SDC) with parameter uncertainties. First, using a Bernoulli distributed sequence, a more universal coupling controller that involves the factor of data transmission delay is proposed. Based on these vectors, an augmented Lyapunov-Krasovskii functional (LKF) is constructed for the CLs, where the LKF is derived as delay-dependent. The LKF is also based on the information of entire sampling interval and non-linear functional vector. Meanwhile, a relaxed second-stage affine Bessel–Legendre inequality (BLIY) is introduced to estimate integral terms generated during the derivation. On account of the improved functional and the relaxed integral inequality, an admissibility criteria via a coupling controller is acquired for the synchronous error system with less conservative and the framework of linear matrix inequalities (LMIs). Then, the memory SDC is designed to synchronize the driving and responding CLs. Finally, a simulation example is provided to verify the validity and superiority of the proposed design scheme.

Keywords

• Lyapunov-Krasovskii functional
• memory sampled-data controller
• Bessel–Legendre inequality
• Lur’e system