Pinning Synchronization of Stochastic T-S Fuzzy Delayed Complex Dynamical Networks with Heterogeneous Impulsive Delays
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Pinning Synchronization of Stochastic T-S Fuzzy Delayed Complex Dynamical Networks with Heterogeneous Impulsive Delays Huilan Yang, Lan Shu, Shouming Zhong, Tao Zhan, and Xin Wang* Abstract: In this paper, we deal with the exponential pinning synchronization (PS) of stochastic T-S fuzzy delayed complex dynamical networks (FDCDNs) with heterogeneous impulsive delays. Unlike the existing works, a fuzzy memory pinning impulsive control (FMPIC) approach is proposed. In order to conquer the difficulties of studying such general system, sufficient conditions that depend on the discrete-delay and distributed-delay impulsive effects are obtained by employing the Lyapunov function, inequality techniques and stochastic analysis theory. It is shown that the PS of FDCDNs can be achieved under the designed FMPIC. Numerical simulation on basis of BA scale-free coupled network is used to illustrate the effectiveness of the theoretical results. Keywords: Complex dynamical networks, heterogeneous impulsive delays, pinning synchronization, T-S fuzzy system.
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INTRODUCTION
Complex dynamical networks (CDNs) have been extensively researched over the past few decades because of their potential applications in various fields of science and engineering, such as sensor networks, communication network and linear and nonlinear programming problems [1–4]. Meanwhile, among all of the dynamical behavior CDNs, synchronization has been a fascinating topic since there exist some collective features in individual node naturally. In addition, time delay is very common in natural and man-made systems, and the existence of time delay usually results in poor performance, including divergence, oscillation, or even instability of CDNs [5–9]. Hence, the synchronization of DCDNs have drawn noticeable attention, and a large number of outstanding results have been reported in [10–15] and references cited therein. It is well known that Takagi-Sugeno (T-S) fuzzy model has good properties in analyzing, synthesizing, and approximating complex dynamical behaviors by a set of IF-THEN rules, which can give local linear representation of the nonlinear system. To this end, many well-known linear system theories can be used to system analysis and synthesis of nonlinear complex systems [16–20]. Moreover, in many real-world and natural processes, the actual sig-
nal transmission between subsystems of coupled CDNs is inevitably subject to stochastic perturbation from various uncertainties [21, 22], which may lead to package loss or transmitted signals not fully being detected and received [23]. Naturally, in order to model more realistic CDNs, we should take full account of all the aspects that are influential in studying the CDNs. So far, this issue has recently attracted increasing attention, many literatures regarding the synchronization of T-S fuzzy CDNs (FCDNs) related to stochastic perturbation have been introduced and have left many fruitful results [24–28]. For example, A trucktrailer system is pr
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