Stochastic synchronization of semi-Markovian jump chaotic Lur’e systems with packet dropouts subject to multiple sampling periods

• Published in: Journal of the Franklin Institute Vol. 356; no. 13; pp. 6899 - 6925
• Main Authors: Li, Qian, Liu, Xinzhi, Zhu, Qingxin, Zhong, Shouming, Cheng, Jun
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.09.2019; Elsevier Science Ltd
• Subjects: Chaos theory; Computer simulation; Dropouts; Linear matrix inequalities; Markov processes; Mathematical analysis; Matrix methods; Probability; Probability theory; Sampling; Stochastic models; Synchronism; Time delay systems
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2019.06.005

This paper is concerned with the problem of stochastic synchronization for semi-Markovian jump chaotic Lur’e systems. Firstly, packet dropouts and multiple sampling periods are both considered. By input-delay approach and then fully considering the probability distribution characteristic of packet dropouts in the modeling, the original system is transformed to a stochastic time-delay system. Secondly, by getting the utmost out of the usable information on the actual sampling pattern, the probability distribution values of stochastic delay taking values in m given intervals can be explicitly obtained. Then, a newly augmented Lyapunov-Krasovskii functional is constructed. Based on that, some sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure the stochastic stability of the error system, and thus, the master system stochastically synchronize with the slave system. Finally, the effectiveness and potential of the obtained results is verified by a simulation example.