Synchronization of cohen-grossberg fuzzy cellular neural networks with time-varying delays

• Main Authors: Manikandan, Munia Samy, Ratnavelu, Kurunathan, Balasubramaniam, Pagavathigounder, Ong, Seng Huat
• Format: Article
• Published: Walter de Gruyter GMBH 2021
• Subjects: QA Mathematics; QC Physics; TA Engineering (General). Civil engineering (General); TJ Mechanical engineering and machinery
• Online Access: http://eprints.um.edu.my/26691/

In this paper, a class of Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with time-varying delays are considered. Initially, the sufficient conditions are proposed to ascertain the existence and uniqueness of the solutions for the considered dynamical system via homeomorphism mapping principle. Then synchronization of the considered delayed neural networks is analyzed by utilizing the drive-response (master-slave) concept, in terms of a linear matrix inequality (LMI), the Lyapunov-Krasovskii (LK) functional, and also using some free weighting matrices. Next, this result is extended so as to establish the robust synchronization of a class of delayed CGFCNNs with polytopic uncertainty. Sufficient conditions are proposed to ascertain that the considered delayed networks are robustly synchronized by using a parameter-dependent LK functional and LMI technique. The restriction on the bounds of derivative of the time delays to be less than one is relaxed. In particular, the concept of fuzzy theory is greatly extended to study the synchronization with polytopic uncertainty which differs from previous efforts in the literature. Finally, numerical examples and simulations are provided to illustrate the effectiveness of the obtained theoretical results.