Hybrid control of stochastic chaotic system based on memristive Lorenz system with discrete and distributed time‐varying delays

Zhang, Bo; Deng, Feiqi; Zhao, Xueyan; Zhang, Chaolong

doi:10.1049/iet-cta.2016.0039

Cited by 8 publications

(4 citation statements)

References 33 publications

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“…Remark 1. e above problem requirement ( 10) is equivalent to find a state feedback controller (7) such that the closed-loop system ( 8) is similar to a linear time-invariant form with the desired eigenstructure; that is, A c is similar to an arbitrary matrix Λ by the proposed parametric approach.…”

Section: Problem Statement and Preliminariesmentioning

confidence: 99%

“…Yu et al present a novel approach through switched control and superheteroclinic loops to linearize two symmetrical equilibria and also give the circuit implementation [6]. Zhang et al design a hybrid controller for the Lorenz system with a piecewise linear memristor and provide criteria to maintain that the trivial solutions are exponentially stable in the mean square [7]. Simultaneously, hidden attractors of the classical Lorenz system are also discussed [8,9].…”

Section: Introductionmentioning

confidence: 99%

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Robust Parametric Control of Lorenz System via State Feedback

Zhang

Liu

2020

Complexity

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This paper considers the parametric control to the Lorenz system by state feedback. Based on the solutions of the generalized Sylvester matrix equation (GSE), the unified explicit parametric expression of the state feedback gain matrix is proposed. The closed loop of the Lorenz system can be transformed into an arbitrary constant matrix with the desired eigenstructure (eigenvalues and eigenvectors). The freedom provided by the parametric control can be fully used to find a controller to satisfy the robustness criteria. A numerical simulation is developed to illustrate the effectiveness of the proposed approach.

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Section: Problem Statement and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Robust Parametric Control of Lorenz System via State Feedback

Zhang

Liu

2020

Complexity

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“…Thus, it is necessary to consider stochastic systems. Of course, there is extensive literature in this area, such as [1][2][3]. Delayed systems are suited to describing such systems that not only depend on the present states, but also on the past states.…”

Section: Introductionmentioning

confidence: 99%

Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps

Deng

Mao

2018

Sci. China Inf. Sci.

Self Cite

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This paper investigates the existence and uniqueness of solutions to neutral stochastic functional differential equations with pure jumps (NSFDEwPJs). The boundedness and almost sure exponential stability are also considered. In general, the classical existence and uniqueness theorem of solutions can be obtained under a local Lipschitz condition and linear growth condition. However, there are many equations that do not obey the linear growth condition. Therefore, our first aim is to establish new theorems where the linear growth condition is no longer required whereas the upper bound for the diffusion operator will play a leading role. Moreover, the pth moment boundedness and almost sure exponential stability are also obtained under some loose conditions. Finally, we present two examples to illustrate the effectiveness of our results.

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“…Bao et al [15,16] studied the complicated dynamical behaviors of the memristor oscillators. Although various memristor-based chaotic systems have been researched in recent years [17][18][19], the research of synchronization between two memristor-based hyperchaotic systems is rarely reported. Because the synchronization of the memristor-based chaotic systems is a challenging problem [20][21][22][23], chaotic behavior, especially the hyperchaotic behavior that has more than one positive Lyapunov exponent, may be uncoordinated and unpredictable.…”

Section: Introductionmentioning

confidence: 99%

Sandwich synchronization of memristor-based hyperchaos systems with time delays

Xiong

et al. 2018

Adv Differ Equ

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In this paper, a memristor-based hyperchaotic system is introduced. Considering time delays between the drive system and the response system in the process of synchronization, this paper designs one kind of flexible sandwich controller, which includes a rest in the sandwich structure, to realize the synchronization between two memristor-based hyperchaotic systems. Based on Lyapunov stability theory, matrix inequality, sandwich control and considering time delays, the exponential synchronization conditions for the memristor-based hyperchaotic systems with time delays via sandwich control are given. Finally, simulation results are displayed to verify the effectiveness and feasibility of this method.

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Hybrid control of stochastic chaotic system based on memristive Lorenz system with discrete and distributed time‐varying delays

Cited by 8 publications

References 33 publications

Robust Parametric Control of Lorenz System via State Feedback

Robust Parametric Control of Lorenz System via State Feedback

Basic theory and stability analysis for neutral stochastic functional differential equations with pure jumps

Sandwich synchronization of memristor-based hyperchaos systems with time delays

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