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Fixed‐time synchronization for discontinuous delayed complex‐valued networks with semi‐Markovian switching and hybrid couplings via adaptive control
Author(s) -
Liu Shujin,
Wu Huaiqin,
Cao Jinde
Publication year - 2020
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3153
Subject(s) - control theory (sociology) , synchronization (alternating current) , controller (irrigation) , differential inclusion , convergence (economics) , nonlinear system , mathematics , lyapunov function , fixed point , computer science , control (management) , topology (electrical circuits) , mathematical optimization , mathematical analysis , physics , combinatorics , quantum mechanics , artificial intelligence , agronomy , economics , biology , economic growth
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.