Guaranteed cost control of synchronisation for uncertain complex delayed networks

Abstract

In this article, the synchronisation for a class of complex delayed dynamical networks with uncertain inner coupling configuration is investigated under the quadratic guaranteed cost control. The coupling delay and nodes delay are considered in the networks. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for the existence of the optimal guaranteed cost control laws are given in terms of linear matrix inequalities. Under these sufficient conditions, the networks are globally asymptotically synchronous, and the optimal upper bound is also guaranteed. Numerical examples are given to illustrate the effectiveness of the proposed methods.

Keywords:

• synchronisation
• guaranteed cost control
• time delays
• uncertainty
• linear matrix inequalities

Acknowledgements

This study was supported by the National Natural Science Foundation of China No. 61004015 and the Research Fund for the Doctoral Programme of Higher Education of China under Grant No. 20090032120034. Furthermore, the authors thank the anonymous referees for their valuable comments and suggestions.