Stabilization of Stochastic Uncertain Complex-Valued Delayed Networks via Aperiodically Intermittent Nonlinear Control

Wang, Pengfei; Bi-guang, Zhang; Su, Huan

doi:10.1109/tsmc.2018.2818129

Cited by 107 publications

(26 citation statements)

References 51 publications

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“…Remark In Theorem , we construct the global Lyapunov function as

V false(t false) = \sum_{k = 1}^{n} c_{k} d_{k} V_{k} false(t false)

, where weights c k and d k are the cofactors of the k th diagonal element of

{scriptL}_{\overset{A}{true}}

and

{scriptL}_{\overset{B}{true}}

, respectively, which shows that the exponential stability of the trivial solution of system has a close relationship with the topological structure of the coupled network. This kind of construction was first proposed by Li et al and was applied to many other systems successfully . Theorem extends this construction to CSNs with multicoupling structure.…”

Section: Global Stability Analysismentioning

confidence: 87%

“…Remark In fact, the assumption on the strong connectedness of considered coupled networks is common . If the strong connectedness is not satisfied, only a part of vertices' stability can be promised (see remark 3 in the work of Li et al for a detailed explanation).…”

Section: Global Stability Analysismentioning

confidence: 99%

“…In 2010, Li et al first explored the stability of CSNs by means of the Lyapunov method and graph‐theoretical technique. After that, based on the work of Li and Shuai, many interesting results were reported for more general CSNs, such as the stability of stochastic CSNs, the stability of complex‐valued CSNs, and the synchronization of CSNs . However, it should be pointed out that the aforementioned works only consider CSNs with single coupling.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Wang

Sun

Fan

et al. 2019

Intl J Robust & Nonlinear

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Summary This paper explores the stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays (ICSNMT). The coupling structure can be nonlinear and the time‐varying delays in which can be different, which can well describe more realistic networks. In order to describe this multicoupling structure, we build ICSNMT on a digraph with multiple arcs. Two cases are discussed, ie, (i) the continuous dynamics is stable and (ii) the impulsive dynamics is stable. Then, by means of impulsive differential inequalities with multiple delays and weighted Lyapunov functions method where the weights are closely linked to the network's topological structure, some stability criteria are established. Then, the theoretical results are illustrated by examples of bidirectional associative memory neural networks and coupled modified Chua's circuits, respectively. The numerical simulations are also carried out to demonstrate the effectiveness and feasibility of our theoretical findings.

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“…Remark In Theorem , we construct the global Lyapunov function as

V false(t false) = \sum_{k = 1}^{n} c_{k} d_{k} V_{k} false(t false)

, where weights c k and d k are the cofactors of the k th diagonal element of

{scriptL}_{\overset{A}{true}}

and

{scriptL}_{\overset{B}{true}}

Section: Global Stability Analysismentioning

confidence: 87%

Section: Global Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Wang

Sun

Fan

et al. 2019

Intl J Robust & Nonlinear

Self Cite

View full text Add to dashboard Cite

show abstract

“…Remark Recently, coupled oscillators systems have attracted much attention, and its dynamical behaviors have been widely studied . It is worth noting that the aforementioned literature only considered single coupling oscillators systems.…”

Section: An Applicationmentioning

confidence: 99%

“…At present, various control strategies have been adopted to realize stability of SMSS, such as pinning control, feedback control, and intermittent control . Intermittent control is a kind of typical discontinuous feedback control strategy requiring control inputs to be activated during some work intervals, which reduces control cost and the amount of transmitted information than continuous feedback control .…”

Section: Introductionmentioning

confidence: 99%

Stabilization of stochastic Markovian switching systems on networks with multilinks based on aperiodically intermittent control: A new differential inequality technique

Yao

Ding

2019

Intl J Robust & Nonlinear

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Summary In this paper, the stabilization problem of stochastic Markovian switching systems on networks with multilinks and time‐varying delays (SMNMT) is investigated via aperiodically intermittent control. At first, a new differential inequality is established for SMNMT, which relaxes the conditions of time‐varying delays compared with existing literature. Different from previous approaches of studying multilinks systems, new differential inequality technique combined with graph theory and Lyapunov method is adopted, based on which two types of sufficient conditions are derived to ensure the stability of SMNMT. The topological structure of multilinks systems on networks, stochastic perturbation, the transition rate of Markov chain, and intermittent control has a great impact on these developed conditions. The theoretical results are applied to stochastic Markovian switching oscillators networks with multilinks (SMONM), and a stabilization criterion of SMONM is derived as well. Finally, a numerical example is shown to illustrate the feasibility of our theoretical results.

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Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

Liu

2018

Asian Journal of Control

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In this paper, finite-time stabilization of coupled systems on networks with time-varying delays (CSNTDs) via periodically intermittent control is studied. Both delayed subsystems and delayed couplings are considered; the self-delays of different subsystems in delayed couplings are not identical. A periodically intermittent controller is designed to stabilize CSNTDs within finite time, and the stabilization duration is closely related to the topological structures of networks. Furthermore, two sufficient criteria are developed to ensure CSNTDs under periodically intermittent control can be stabilized within finite time by using an approach that combines the Lyapunov method with Kirchhoff's Matrix Tree Theorem. Then finite-time stabilization of coupled oscillators with time-varying delays is given as a practical application and sufficient criteria is obtained. Finally, a numerical simulation is proposed to support our results and show the effectiveness of the controller.

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Stabilization of Stochastic Uncertain Complex-Valued Delayed Networks via Aperiodically Intermittent Nonlinear Control

Cited by 107 publications

References 51 publications

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Stability of impulsive coupled systems on networks with both multicoupling structure and time‐varying delays

Stabilization of stochastic Markovian switching systems on networks with multilinks based on aperiodically intermittent control: A new differential inequality technique

Finite‐Time Stabilization of Coupled Systems on Networks with Time‐Varying Delays via Periodically Intermittent Control

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