Using partial sampled-data information for synchronization of chaotic Lur’e systems and its applications: an interval-dependent functional method

Abstract

This paper is concerned with the synchronization problem of chaotic Lur’e systems by using partial sampled-data information. First, a useful lemma is established on the basis of discrete-time Lyapunov theory and interval estimate methods, which contributes to the stability of partial sampled-data control (PSC) systems. According to the features of the designed control scheme, a single-interval-dependent functional and a double-intervals-dependent functional are constructed by utilizing the corresponding interval information, respectively. Unlike the previous Lyapunov functional methods, the proposed functionals are essentially continuous and then some additional constraint conditions are removed. Then, based on several inequality methods, two sufficient criteria dependent on the controller gain, sampling period, and allowable data loss ratio (ADLR), are respectively developed to guarantee the global synchronization of Lur’e systems. Additionally, the quantitative analysis about the ADLR is discussed. Compared with the existing results, the developed interval-dependent functional techniques are beneficial to enlarging the ADLR. Finally, illustrative examples and an application to image encryption are given to demonstrate the advantages and effectiveness of the proposed control strategy.