Rakkiyappan R, Sakthivel N, Cao J. Stochastic sampled-data control for synchronization of complex dynamical networks with control packet loss and additive time-varying delays.
Neural Netw 2015;
66:46-63. [PMID:
25797504 DOI:
10.1016/j.neunet.2015.02.011]
[Citation(s) in RCA: 63] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/23/2014] [Revised: 02/21/2015] [Accepted: 02/22/2015] [Indexed: 10/23/2022]
Abstract
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.
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