H ∞ Synchronization of Directed Complex Dynamical Networks with Mixed Time-Delays and Switching Structures

This paper considers the asymptotical synchronization and H ∞ synchronization for coupled neutral-type delay partial differential systems (NDPDSs). First, we construct a coupled synchronization error dynamic. Using the method of nonsingular matrix transformation, we decouple these coupled synchronization error dynamical systems. Then we study the asymptotical stability of the decoupled synchronization error dynamical systems through the Lyapunov-Krasovskii functional method, which implies the asymptotical synchronization of the coupled NDPDSs. Furthermore, when external disturbances enter the coupled NDPDSs, the H ∞ synchronization problem is also considered. The equivalence between the H ∞ stability of decoupled synchronization error dynamical systems and the H ∞ synchronization of coupled NDPDSs is proved by rigorous mathematical analysis. Then the criterion for the H ∞ stabilization is presented, which guarantees the H ∞ synchronization of the coupled NDPDSs. Moreover, as a remarkable difference between the ordinary differential systems and partial differential systems, the effect of the spatial domain on the synchronization is revealed through the obtained criteria. At last, numerical examples are given to illustrate the correctness of our results.

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“…The boundary conditions and initial values are given by (27) and (28), and the synchronization function is also given by (29) and (30).…”

Section: Remark 1 From the Conditionsmentioning

confidence: 99%

Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

Zhao

Yao

2015

Circuits Syst Signal Process

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“…Motivated by the H 1 control, the H 1 synchronization was brought out to deal with the synchronization of coupled systems with external disturbances [14]. From then on, many interesting results were reported on the H 1 synchronization, see, for example, [15][16][17][18][19][20][21]. In [16], the authors considered the H 1 synchronization for coupled chaotic systems by dynamic feedback method.…”

Section: Introductionmentioning

confidence: 99%

“…In [16], the authors considered the H 1 synchronization for coupled chaotic systems by dynamic feedback method. In [17], the authors dealt with the H 1 synchronization of stochastic coupled delay systems with Markovian switching, in which both discrete time delay and distributed time delay were studied. The H 1 synchronization of second-order neutral delay systems was also investigated in [18].…”

Section: Introductionmentioning

confidence: 99%

H∞ synchronization of coupled delay partial differential systems via nonsingular transformation method

Wang

et al. 2015

Applied Mathematical Modelling

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a b s t r a c tThis paper considers the H 1 synchronization of coupled delay partial differential systems (PDSs). By using the nonsingular transformation method, the coupled systems are decoupled to simplify the complex H 1 synchronization problem of coupled delay PDSs. The equivalence of the H 1 synchronization for original coupled delay PDSs and the H 1 stabilization of transformed decoupled delay PDSs is rigorously verified. Sufficient conditions are obtained to guarantee the H 1 synchronization. These sufficient conditions also reflect the effect of spatial domain on the H 1 synchronization. Moreover, when the external disturbances disappear, the asymptotical synchronization is studied. The relationship between the H 1 synchronization and the asymptotical synchronization is also presented. At last, an example is given to illustrate the correctness of our results.

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“…The applications include economic systems, modeling production systems, and other practical systems. Recently, considerable research attention has been paid to CDNs with Markovian jumping parameters . Robust stabilization of stochastic Markovian jumping dynamical networks with mixed delays was discussed in .…”

Section: Introductionmentioning

confidence: 99%

Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays

Li¹,

Rakkiyappan²,

Sakthivel³

2014

Asian Journal of Control

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This paper studies the problem of non-fragile synchronization control for Markovian jumping complex dynamical networks with probabilistic time-varying coupling delays. By constructing a new Lyapunov-Krasovskii functional (LKF) and combining the reciprocal convex technique, sufficient conditions for the complex dynamical networks to be globally asymptotically synchronized in the mean square sense are derived. The probability distribution of the delays have been proposed and delay probability-distribution-dependent conditions are derived in the form of linear matrix inequalities (LMIs). The derived conditions depend not only on the size of the delay but also on the probability of the delay taking values in some intervals. Further, a non-fragile synchronization controller is proposed. Finally, a numerical example is given to demonstrate the effectiveness of the proposed methods.

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H ∞ Synchronization of Directed Complex Dynamical Networks with Mixed Time-Delays and Switching Structures

Cited by 28 publications

References 37 publications

Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

Synchronization of Coupled Neutral-Type Delay Partial Differential Systems

H∞ synchronization of coupled delay partial differential systems via nonsingular transformation method

Non‐Fragile Synchronization Control For Markovian Jumping Complex Dynamical Networks With Probabilistic Time‐Varying Coupling Delays

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