Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory

Kaviarasan, B.; Sakthivel, R.; Lim, Yongdo

doi:10.1016/j.neucom.2015.12.071

Cited by 99 publications

(28 citation statements)

References 43 publications

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“…Further, by applying Jensen's single integral inequality [6] to the integral terms in (16), we can get the following inequalities:…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, based on Lemma 2 in [6], for any positive scalar 1 , the right-hand side of (20) can equivalently be written as…”

Section: Resultsmentioning

confidence: 99%

“…It should be noted that, so far in the literature, several control approaches have been proposed for the synchronization problem of several CDNs [3][4][5][6], wherein the interconnection topology among the nodes are assumed to be fixed. However, in practice, this assumption is practically difficult or even impossible.…”

Section: Remarkmentioning

confidence: 99%

“…It should be mentioned that the analysis of dynamical behaviors of CDNs has become a hot research topic in recent years. Among many dynamical behaviors, synchronization phenomenon is the most important behavior and several interesting and efficient methodologies have been developed in the literature to solve the synchronization problem of various kinds of CDNs; for instance, see [3][4][5][6][7]. In [4], the problem of inner synchronization of a CDN has been investigated by considering two different types of guaranteed cost dynamic feedback controllers, where the control gains corresponding to two feedback controllers have different dimensions subject to the topological structure of the CDN.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Finite‐Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi‐Markov Switching Outer Coupling

Sakthivel

Kaviarasan

et al. 2018

Complexity

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The problem of robust nonfragile synchronization is investigated in this paper for a class of complex dynamical networks subject to semi-Markov jumping outer coupling, time-varying coupling delay, randomly occurring gain variation, and stochastic noise over a desired finite-time interval. In particular, the network topology is assumed to follow a semi-Markov process such that it may switch from one to another at different instants. In this paper, the random gain variation is represented by a stochastic variable that is assumed to satisfy the Bernoulli distribution with white sequences. Based on these hypotheses and the Lyapunov-Krasovskii stability theory, a new finite-time stochastic synchronization criterion is established for the considered network in terms of linear matrix inequalities. Moreover, the control design parameters that guarantee the required criterion are computed by solving a set of linear matrix inequality constraints. An illustrative example is finally given to show the effectiveness and advantages of the developed analytical results.

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“…Further, by applying Jensen's single integral inequality [6] to the integral terms in (16), we can get the following inequalities:…”

Section: Resultsmentioning

confidence: 99%

“…Moreover, based on Lemma 2 in [6], for any positive scalar 1 , the right-hand side of (20) can equivalently be written as…”

Section: Resultsmentioning

confidence: 99%

Section: Remarkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Finite‐Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi‐Markov Switching Outer Coupling

Sakthivel

Kaviarasan

et al. 2018

Complexity

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show abstract

“…It generally requires the derivative of a time-varying delay. This derivative should be smaller than 1 [20][21][22][23][24] or should be localized in one boundary [25][26][27]. Meanwhile, the derivation of a rapidly changing time-varying delay may fail, and thus these methods are ineffective.…”

Section: Introductionmentioning

confidence: 99%

New results of exponential synchronization of complex network with time-varying delays

Luo¹,

Ling²,

Cheng³

et al. 2019

Adv Differ Equ

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In this study, we elucidated the exponential synchronization of a complex network system with time-varying delay. Then the exponential synchronization control of several types of complex network systems with time-varying delay under no requirements of delay derivable were explored. The dynamic behavior of a system node shows time-varying delays. Thus, to derive suitable conditions for the exponential synchronization of different complex network systems, we designed a linear feedback controller for linear coupling functions, using the Lyapunov stability theory, Razumikhin theorem, and Newton-Leibniz formula. The exponential damping rates for the exponential synchronization of different complex network systems were then estimated. Finally, we validated our conclusions through a numerical simulation.

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Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller

Zhang

Wang

et al. 2019

Asian Journal of Control

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This paper investigates the generalized projective synchronization (GPS) among the nodes within a complex dynamical network (CDN). Multiple characteristics of realistic networks are simultaneously considered in our network model. First, one crucial node is introduced into our CDN, which behaves like a leader and exists in many practical networks. Second, the commonalities between the crucial node and every other node are discussed and they are embodied in the network model. Third, our CDN is composed of different dimensional nodes and has an overall time‐varying coupling strength. Furthermore, in order to describe more synchronous phenomena, the exponential generalized projective synchronization (EGPS) and asymptotic generalized projective synchronization (AGPS) are defined. The main objective of this paper is to design an effective but simple decentralized controller for the crucial node such that our network realizes GPS. Based on rigorous theoretical derivations, EGPS and AGPS schemes are respectively proposed according to whether the overall coupling strength is certain or adaptive. Few previous studies have focused on this. It is worth pointing out that both the control input and the adaptive law of the coupling strength in this paper only lie in the information of the crucial node, which implies the significance of the crucial node to some extent. Finally, the effectiveness and feasibility of our theoretical results are verified by two numerical simulation examples.

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Synchronization of complex dynamical networks with uncertain inner coupling and successive delays based on passivity theory

Cited by 99 publications

References 43 publications

Finite‐Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi‐Markov Switching Outer Coupling

Finite‐Time Nonfragile Synchronization of Stochastic Complex Dynamical Networks with Semi‐Markov Switching Outer Coupling

New results of exponential synchronization of complex network with time-varying delays

Generalized projective synchronization for networks with one crucial node and different dimensional nodes via a single controller

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