RESEARCH ARTICLE
Fixed-time synchronization for discontinuous delayed complex-valued networks with semi-Markovian switching and hybrid couplings via adaptive control
Shujin Liu,
Huaiqin Wu,
Jinde Cao,
Shujin Liu
School of Science, Yanshan University, Qinhuangdao, China
Search for more papers by this authorCorresponding Author
Huaiqin Wu
School of Science, Yanshan University, Qinhuangdao, China
Correspondence
Huaiqin Wu, School of Science, Yanshan University, Qinhuangdao, Hebei 066001, China.
Email: [email protected]
Search for more papers by this authorJinde Cao
School of Mathematics, Southeast University, Nanjing, China
Search for more papers by this authorShujin Liu,
Huaiqin Wu,
Jinde Cao,
Shujin Liu
School of Science, Yanshan University, Qinhuangdao, China
Search for more papers by this authorCorresponding Author
Huaiqin Wu
School of Science, Yanshan University, Qinhuangdao, China
Correspondence
Huaiqin Wu, School of Science, Yanshan University, Qinhuangdao, Hebei 066001, China.
Email: [email protected]
Search for more papers by this authorJinde Cao
School of Mathematics, Southeast University, Nanjing, China
Search for more papers by this authorFunding information: High Level Talent Project of Hebei Province of China, C2015003054; Postgraduate Innovation Project of Hebei Province of China, CXZZSS2020041; the Natural Science Foundation of Hebei Province of China, A2018203288
Summary
In this article, the global fixed-time synchronization issue is considered for semi-Markovian switching discontinuous complex-valued dynamical networks (CVDNs) with hybrid couplings and time-varying delays, in which CVDNs are not divided into two real value systems, contrary to existing literature. First, a new fixed-time convergence principle for complex-valued nonlinear system with semi-Markovian switching is developed. Second, to realize the fixed-time synchronization, the state feedback controller with integral term and adaptive controller are designed, respectively. Under the complex-valued differential inclusions framework, by utilizing Lyapunov-Krasovskii functional method and inequality analysis technique, the global fixed-time synchronization conditions are addressed in terms of linear matrix inequalities. Finally, two numerical simulations are given to illustrate the validity of the presented theoretical results.
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