Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays

• Published in: Neural networks 2015-06, Vol.66, p.46-63
• Main Authors: Rakkiyappan, R., Sakthivel, N., Cao, Jinde
• Format: Article
• Language: English
• Subjects: Additive time-varying delays; Algorithms; Complex dynamical networks; Control packet loss; Neural Networks (Computer); Reciprocally convex approach; Stochastic Processes; Stochastic sampled-data; Time Factors
• ISSN: 0893-6080; 1879-2782
• DOI: 10.1016/j.neunet.2015.02.011

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov–Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen’s inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen’s inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.