Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control

Yang, Huilan; Wang, Xin; Zhong, Shouming; Shu, Lan

doi:10.1016/j.amc.2017.09.019

Cited by 42 publications

(22 citation statements)

References 34 publications

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“…Taking (43) into account, we have P 12 = 0 and P 11 > 0. Then pre-multiplying and postmultiplying (43) byT T and T, respectively, it is easy to obtain sym(A T 22 P 22 ) < 0 showing that A 22 is nonsingular.…”

Section: Resultsmentioning

confidence: 99%

State bounding estimation for a linear continuous-time singular system with time-varying delay

Xiao

2019

Adv Differ Equ

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Section: Resultsmentioning

confidence: 99%

State bounding estimation for a linear continuous-time singular system with time-varying delay

Xiao

2019

Adv Differ Equ

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“…In order to overcome the double difficulties caused by time delay and positive interest rate, the author has to adopt double control methods: impulse control and regional control. Recall that impulsive effects of complex dynamic systems have been investigated [13][14][15][16][17][18][19][20]. The impulses may lead to the instability or stability of the system depending on the magnitude of the impulses.…”

Section: Remarkmentioning

confidence: 99%

“…Let u be a solution of the system (10), then one can conclude from (16), the Gauss formula, and the Neumann zero boundary condition that:…”

Section: Globally Exponential Stability Of Q 1 With the Positive Intementioning

confidence: 99%

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Rao

2019

Mathematics

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The intrinsic instability of the financial system itself results in chaos and unpredictable economic behavior. To gain the globally asymptotic stability of the equilibrium point with a positive interest rate of the chaotic financial system, pulse control is sometimes very necessary and is employed in this paper to derive the globally exponential stability of financial system. It should be pointed out that the delayed feedback model brings an essential difficulty so that the regional control method has to be adopted. In this paper, the author firstly employs impulsive control, regional control, the Lyapunov function technique, and variational methods to derive the stochastically globally asymptotic stability criterion of the economic balance point with a positive interest rate for a delayed feedback financial system with Markovian jumping and partially unknown transition rates. Besides, the mathematical induction method and the proof by contradiction are applied synthetically to deduce the globally exponential stability of the equilibrium point with a positive interest rate for the impulsive financial system without time-delays. Moreover, numerical examples illustrate that under suitable data conditions on the two main criteria mentioned above, the interest rates are positive decimals when the financial system reaches stability, which means better economic significance.

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“…Li et al [34] found that time-delayed impulses may contribute to the stabilization of delayed systems by restricting the impulse interval and impulsive gain. Subsequently, Yang et al [35] used this result to design a distributed delayed impulsive controller to investigate the exponential synchronization for nonlinear complex dynamical systems. However, few work considered dynamical systems with hybrid impulses and hybrid delayed impulses, including simultaneous stabilizing and destabilizing cases.…”

Section: Introductionmentioning

confidence: 99%

Halanay-type inequality with delayed impulses and its applications

Wang

Lou

2019

Sci. China Inf. Sci.

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In this study, some properties of a novel Halanay-type inequality that simultaneously contains impulses and delayed impulses are investigated. Two concepts with respect to average impulsive gain are proposed to describe hybrid impulsive strength and hybrid delayed impulsive strength. Then, using the obtained results, two stability criteria are derived for the linear systems with impulses and delayed impulses. It is found that the stability of impulsive systems is robust with respect to delayed impulses of which the magnitude strength is relatively small. Whereas, if the impulse strength is small, the time-delayed impulses can also promote the stability of unstable systems. Two numerical examples are employed to illustrate the efficiency of our results.

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Synchronization of nonlinear complex dynamical systems via delayed impulsive distributed control

Cited by 42 publications

References 34 publications

State bounding estimation for a linear continuous-time singular system with time-varying delay

State bounding estimation for a linear continuous-time singular system with time-varying delay

Global Stability of a Markovian Jumping Chaotic Financial System with Partially Unknown Transition Rates under Impulsive Control Involved in the Positive Interest Rate

Halanay-type inequality with delayed impulses and its applications

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