Stabilisation of stochastic delayed systems with Lévy noise on networks via periodically intermittent control

Xu, Yang; Zhou, Hui; Li, Wenxue

doi:10.1080/00207179.2018.1479538

Cited by 58 publications

(35 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark Notice that if there is a single link (i.e., l = 1), the global Lyapunov function

V (t, e) = \sum_{k = 1}^{n} \prod_{i = 1}^{m} d_{k}^{(i)} V_{k} (t, e_{k})

will become

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

, where d k denotes the cofactor of the k th diagonal element of Laplacian matrix of digraph

((), scriptG, A)

, which is similar to that in other studies . Thus, our results can seem as a generalization of theirs to some extent.…”

Section: Global Synchronization Analysissupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

“…The last decade has witnessed the extensive researches for dynamics of complex networks (CNs) since CNs can characterize a quantity of real systems, such as biological and artificial neural networks, 1 complex ecosystems, 2 epidemic models, [3][4][5] and coupled oscillators on lattices. 6 One of the major topics drawing considerable concerns is synchronization of CNs. Currently, many results on synchronization analysis of CNs have been achieved for the strong demands from diverse sorts of fields in parallel image processing, pattern recognition, and secure communication.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

2019

Math Methods in App Sciences

Self Cite

View full text Add to dashboard Cite

This paper concentrates on the global synchronization of the fractional‐order multi‐linked complex network (FMCN) via periodically intermittent control. It should be stressed that periodically intermittent control is employed to the FMCN for the first time. Moreover, the network is defined on digraphs with different weights, and two situations on topological structure of the network are discussed, including each digraph being strongly connected, and the biggest one being strongly connected. Based on Lyapunov method and graph theory, some synchronization criteria are obtained under two situations. And, the obtained synchronization criteria have a close relationship with the order of fractional‐order derivative, coupling strength, control gain, control rate, and control period. Besides, for practicability, theoretical results are applied to studying the synchronization of fractional‐order multi‐linked chaotic systems, and some sufficient conditions are provided. For a special case, fractional‐order multi‐linked Lorenz chaotic systems, numerical simulations are given to indicate the feasibility of theoretical results and the effectiveness of control strategy.

show abstract

“…Remark Notice that if there is a single link (i.e., l = 1), the global Lyapunov function

V (t, e) = \sum_{k = 1}^{n} \prod_{i = 1}^{m} d_{k}^{(i)} V_{k} (t, e_{k})

will become

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

, where d k denotes the cofactor of the k th diagonal element of Laplacian matrix of digraph

((), scriptG, A)

, which is similar to that in other studies . Thus, our results can seem as a generalization of theirs to some extent.…”

Section: Global Synchronization Analysissupporting

confidence: 62%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

2019

Math Methods in App Sciences

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

View full text Add to dashboard Cite

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.

show abstract

Stability analysis of stochastic differential systems with state‐dependent delay subject to average‐delay impulses

Xu,

Zhang,

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

In this paper, we study the stochastic weak local exponential stability of stochastic differential systems with state‐dependent delay (SDD) subject to average‐delay impulses by using Lyapunov–Krasovskii functional and stochastic analytical skill. Unlike time‐dependent delay discussed in the previous literature, we introduce SDD in impulsive stochastic differential systems, where SDD is a stochastic variable associated with system state, consequently leading to an indeterminate delay boundary. Our findings reveal that when destabilizing delayed impulses satisfying specific conditions are generated, the stability of stochastic differential systems with destabilizing delayed impulses and stable continuous stochastic dynamics can still be maintained. Additionally, if stable delayed impulses satisfy certain conditions, stability of the systems under consideration can also be achieved, irrespective of the stable status on the continuous stochastic dynamics. Finally, two examples are given to demonstrate the validity of theoretical results.

show abstract

Stabilisation of stochastic delayed systems with Lévy noise on networks via periodically intermittent control

Cited by 58 publications

References 51 publications

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

Synchronization for fractional‐order multi‐linked complex network with two kinds of topological structure via periodically intermittent control

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

Stability analysis of stochastic differential systems with state‐dependent delay subject to average‐delay impulses

Contact Info

Product

Resources

About