H∞ Synchronization of Uncertain Chaotic Lur’e Systems with Time-varying Delay via Stochastic Sampling

• Published in: International journal of control, automation, and systems Vol. 20; no. 4; pp. 1111 - 1121
• Main Authors: Zhao, Hanxiao, Zhang, Jiayong, Li, Wei, Ge, Chao, Liu, Yajuan
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.04.2022; Springer Nature B.V
• Subjects: Control; Delay; Engineering; H-infinity control; Linear matrix inequalities; Mechatronics; Parameter uncertainty; Probability theory; Random sampling; Regular Papers; Robotics; Synchronism; Time varying control; stochastic sampling; Chaotic Lur’e system; synchronization; parameter uncertainty
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-020-0601-8

In this article, the problem of H ∞ synchronization for uncertain chaotic systems with time-varying delay controlled by random sampling is considered. The variable sampling period is assumed to switch stochastically between different values with given probability. In addition, the disturbance and the parameter uncertainty that may occur in many actual system are taken into account. With the help of input delay method, the chaotic Lur’e systems (CLSs) with probability sampling is converted to a continuous system. Then, based on the Lyapunov-Krasovskii functional (LKF) theory, a novel LKF is proposed. By using the reciprocal convex method, sufficient conditions are obtained to guarantee the stability of the error system and to reduce the influence of external disturbances under the condition of bounded H ∞ norm. By solving a series of linear matrix inequalities (LMIs) which are obtained, the corresponding sampled data controller can be obtained. Finally, a numerical example is used to illustrate the superiority and effectiveness of proposed method.