Robust control for synchronization of singular complex delayed networks with stochastic switched coupling

Abstract

This paper investigates the robust H _∞ control of synchronization for uncertain singular complex delayed networks with stochastic switched coupling. The switched coupling is dependent on a continuous time Markovian process. Based on Lyapunov–Krasovskii stability theory, sufficient conditions for the existence of the H _∞ control laws are given in terms of linear matrix inequalities, which ensure robustly global mean-square synchronization and a prescribed H _∞ disturbance attenuation level for the resulting closed-loop complex networks. Numerical examples are given to illustrate the effectiveness of the proposed method.

Keywords:

• singular complex networks
• Markovian process
• H _∞ control
• time delays
• linear matrix inequalities

2000 AMS Subject Classifications :

• 34H05
• 93D09
• 93E15

Acknowledgements

The authors thank the anonymous referees for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China No. 61004015, the Research Fund for the Doctoral Program of Higher Education of China under Grant 20090032120034, the Program for New Century Excellent Talents in Universities of China, and the Program for Changjiang Scholars and Innovative Research Team in University of China No. IRT1028.