Synchronization criteria for T-S fuzzy singular complex dynamical networks with Markovian jumping parameters and mixed time-varying delays using pinning control

Document Type : Research Paper


1 Department of Mathematics, Thiruvalluvar University, Vellore - 632 115, Tamilnadu, India

2 Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia.


In this paper, we are discuss about the issue of synchronization for singular complex dynamical networks with Markovian jumping parameters and additive time-varying delays through pinning control by Takagi-Sugeno (T-S) fuzzy theory.
The complex dynamical systems consist of m nodes and the systems switch from one mode to another, a Markovian chain with glorious transition probability. Based on the control strategies are designed, the singular complex dynamical
networks are synchronized. A new class of Lyapunov-Krasovskii functional, which contains integral terms is constructed to derive the stability criteria. Some sufficient conditions for synchronization in the form of linear matrix inequality
(LMI) approach. Finally, numerical example is presented to support the main results of this paper.