Approximate synchronization of uncertain complex delayed networks with non-identical nodes

Abstract

In this article, a delayed complex network model with non-identical nodes is established, where the mismatched uncertain parameters are involved in each node. The concept of approximate synchronization is proposed. A linear feedback controller is designed and a sufficient condition for boundedness of the synchronous error is presented in terms of linear matrix inequalities. A pseudoconvex optimization problem for minimizing the upper bound of the synchronous error is proposed. Furthermore, an iterative algorithm involving convex problem is designed to solve this pseudoconvex optimization problem and obtain the globally optimal solution, by which the approximate synchronization is achieved. At last, two numerical examples are given to show the effectiveness of the proposed criterion.

Keywords:

• complex network
• approximate synchronization
• time delay
• uncertainty
• linear matrix inequality
• pseudoconvex optimization

2000 AMS Subject Classifications:

• 34H05
• 90C25
• 93D09

Acknowledgements

This work was supported by the National Nature Science Foundation of China No. 61004015, the Program for New Century Excellent Talents in Universities of China (NECT-11-0377), and the Program for Changjiang Scholars and Innovative Research Team in University of China (IRT 1028).