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Journal articles on the topic 'Time delayed feedback control (TDFC)'

Author: Grafiati

Published: 22 July 2024

Last updated: 31 July 2025

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1

BANERJEE, TANMOY, and B. C. SARKAR. "CONVENTIONAL AND EXTENDED TIME-DELAYED FEEDBACK CONTROLLED ZERO-CROSSING DIGITAL PHASE LOCKED LOOP." International Journal of Bifurcation and Chaos 22, no. 12 (2012): 1230044. http://dx.doi.org/10.1142/s0218127412300443.

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This article investigates the effect of the conventional and extended time-delayed feedback control techniques of chaos control on a first-order positive zero-crossing digital phase locked loop (ZC1-DPLL) using local stability analysis, two-parameter bifurcation studies and two-parameter Lyapunov exponent spectrum. Starting from the nonlinear dynamics of a ZC1-DPLL, we at first explore the time-delayed feedback control (TDFC) algorithm on a ZC1-DPLL in the parameter space. A condition for the optimum value of the system control parameter is derived analytically for a TDFC based ZC1-DPLL. Next,

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2

ROBERT, B., H. H. C. IU, and M. FEKI. "ADAPTIVE TIME-DELAYED FEEDBACK FOR CHAOS CONTROL IN A PWM SINGLE PHASE INVERTER." Journal of Circuits, Systems and Computers 13, no. 03 (2004): 519–34. http://dx.doi.org/10.1142/s0218126604001568.

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Many power converters exhibit chaotic behaviors and bifurcations when conventional feedback corrector are badly tuned or when parameters vary. Time-Delayed Feedback Control (TDFC) can be used to stabilize them using a state feedback delayed by the period of the unstable orbit (UPO) to be stabilized. An obvious advantage of this method is the robustness because it does not require the knowledge of an accurate model but only the period of the target UPO. In this paper, TDFC is applied to a PWM current-programmed single phase inverter concurrently with a proportional corrector in order to avoid b

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3

Erneux, T., G. Kozyreff, and M. Tlidi. "Bifurcation to fronts due to delay." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 368, no. 1911 (2010): 483–93. http://dx.doi.org/10.1098/rsta.2009.0228.

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The stability of a steady-state front (kink) subject to a time-delayed feedback control (TDFC) is examined in detail. TDFC is based on the use of the difference between system variables at the current moment of time and their values at some time in the past. We first show that there exists a bifurcation to a moving front. We then investigate the limit of large delays but weak feedback and obtain a global bifurcation diagram for the propagation speed. Finally, we examine the case of a two-dimensional front with radial symmetry and determine the critical radius above which propagation is possibl

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4

Sun, Xiuting, Yipeng Qu, Feng Wang, and Jian Xu. "Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression." Applied Mathematics and Mechanics 44, no. 10 (2023): 1629–50. http://dx.doi.org/10.1007/s10483-023-3038-6.

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AbstractThe effects of time-delayed vibration absorber (TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given, and the results show that the introduction of time-delayed feedback control (TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad

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5

ROBERT, B., M. FEKI, and H. H. C. IU. "CONTROL OF A PWM INVERTER USING PROPORTIONAL PLUS EXTENDED TIME-DELAYED FEEDBACK." International Journal of Bifurcation and Chaos 16, no. 01 (2006): 113–28. http://dx.doi.org/10.1142/s0218127406014629.

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Pulse width modulation (PWM) current-mode single phase inverters are known to exhibit bifurcations and chaos when parameters vary or if the gain of the proportional controller is arbitrarily increased. Our aim in this paper is to show, using control theory and numerical simulations, how to apply a method to stabilize the interesting periodic orbit for larger values of the proportional gain. To accomplish this aim, a time-delayed feedback controller (TDFC) is used in conjunction with the proportional controller in its simple form as well as in its extended form (ETDFC). The main advantages of t

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BANERJEE, TANMOY, BISHWAJIT PAUL, and B. C. SARKAR. "BIFURCATION, CHAOS AND THEIR CONTROL IN A TIME-DELAY DIGITAL TANLOCK LOOP." International Journal of Bifurcation and Chaos 23, no. 08 (2013): 1330029. http://dx.doi.org/10.1142/s0218127413300292.

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This paper reports the detailed parameter space study of the nonlinear dynamical behaviors and their control in a time-delay digital tanlock loop (TDTL). At first, we explore the nonlinear dynamics of the TDTL in parameter space and show that beyond a certain value of loop gain parameter the system manifests bifurcation and chaos. Next, we consider two variants of the delayed feedback control (DFC) technique, namely, the time-delayed feedback control (TDFC) technique, and its modified version, the extended time-delayed feedback control (ETDFC) technique. Stability analyses are carried out to f

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7

Wang, Deli, Wei Xu, Zhicong Ren, and Haiqing Pei. "Maximal Lyapunov Exponents and Steady-State Moments of a VI System based Upon TDFC and VED." International Journal of Bifurcation and Chaos 29, no. 11 (2019): 1950155. http://dx.doi.org/10.1142/s0218127419501554.

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This paper focuses on the investigation of a vibro-impact (VI) system based upon time-delayed feedback control (TDFC) and visco-elastic damping (VED) under bounded random excitations. A pretreatment for the TDFC and VED is necessary. A further simplification for the system is achieved by introducing the mirror image transformation. The averaging approach is adopted to analyze the above system relying on a parametric principal resonance consideration. By means of the first kind of a modified Bessel function, explicit asymptotic formulas for the maximal Lyapunov exponent (MLE) are given to exami

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8

Xiao, Jianli, Hanli Xiao, Xinchang Zhang, and Xiang You. "Stability, Bifurcation, and Chaos Control of Two-Sided Market Competition." International Journal of Computer Games Technology 2022 (August 17, 2022): 1–10. http://dx.doi.org/10.1155/2022/6006450.

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Benefitting from the popular uses of internet technologies, two-sided market has been playing an increasing prominent role in modern times. Users and developers can interact with each other through two-sided platforms. The two-sided market structure has been investigated profoundly. Through building a dynamics two-sided market model with bounded rational, stability conditions of the two-sided market competition system are presented. With the help of bifurcation diagram, Lyapunov exponent, and strange attractor, the stability of the two-sided market competition model is simulated. At last, we u

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Xiao, Jianli, and Hanli Xiao. "The Complexities in the R&D Competition Model with Spillover Effects in the Supply Chain." Complexity 2024 (February 28, 2024): 1–15. http://dx.doi.org/10.1155/2024/3152363.

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This study aims to investigate the research and development (R&D) competition within the supply chain, focusing on two aspects: R&D competition at the manufacturing level and competition in pricing strategies. This paper establishes a dynamic game model of R&D competition, comprising two manufacturers and two retailers, with both manufacturers exhibiting bounded rationality. The key findings are as follows: (1) an increase in the adjustment speed positively affects the chaotic nature of the R&D competition system, leading to a state of disorder. This chaotic state has adverse i

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10

Vasegh, Nastaran, and Ali Khaki Sedigh. "Chaos control via TDFC in time-delayed systems: The harmonic balance approach." Physics Letters A 373, no. 3 (2009): 354–58. http://dx.doi.org/10.1016/j.physleta.2008.11.050.

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11

Zhang, Jinke, Xiaojie Wu, Lvshuai Xing, Chao Zhang, Herbert Iu, and Tyrone Fernando. "Bifurcation Analysis of Five-Level Cascaded H-Bridge Inverter Using Proportional-Resonant Plus Time-Delayed Feedback." International Journal of Bifurcation and Chaos 26, no. 11 (2016): 1630031. http://dx.doi.org/10.1142/s0218127416300317.

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In this paper, a traditional five-level cascaded H-bridge inverter is studied and regulated by a proportional-resonant (PR) controller. In order to extend the range of the gain of PR controller, for the purpose of achieving a fast response, a time-delayed feedback controller (TDFC) is used. Similar to the pulse width modulation (PWM) current-mode single phase H-bridge inverter that exhibits bifurcation and chaos when parameters vary, we demonstrate for the first time that the cascaded H-bridge inverter also shows similar features. From the perspective of a discontinuous map, the cascaded H-bri

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12

Schöll, Eckehard, Judith Lehnert, Thomas Dahms, Anton Selivanov, and Alexander L. Fradkov. "Adaptive time-delayed feedback control." IEICE Proceeding Series 1 (March 17, 2014): 674–77. http://dx.doi.org/10.15248/proc.1.674.

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13

Biggs, James D., and Colin R. McInnes. "Time-Delayed Feedback Control in Astrodynamics." Journal of Guidance, Control, and Dynamics 32, no. 6 (2009): 1804–11. http://dx.doi.org/10.2514/1.43672.

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14

Just, Wolfram, Thomas Bernard, Matthias Ostheimer, Ekkehard Reibold, and Hartmut Benner. "Mechanism of Time-Delayed Feedback Control." Physical Review Letters 78, no. 2 (1997): 203–6. http://dx.doi.org/10.1103/physrevlett.78.203.

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15

Just, Wolfram, Ekkehard Reibold, Harmut Benner, Krzysztof Kacperski, Piotr Fronczak, and Janusz Hołyst. "Limits of time-delayed feedback control." Physics Letters A 254, no. 3-4 (1999): 158–64. http://dx.doi.org/10.1016/s0375-9601(99)00113-9.

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16

Mehendale, Charudatta S., and Karolos M. Grigoriadis. "CONTROL OF TIME-DELAYED LPV SYSTEMS USING DELAYED FEEDBACK." IFAC Proceedings Volumes 38, no. 1 (2005): 249–54. http://dx.doi.org/10.3182/20050703-6-cz-1902.00612.

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17

Block, M., and E. Schöll. "Time delayed feedback control in growth phenomena." Journal of Crystal Growth 303, no. 1 (2007): 30–33. http://dx.doi.org/10.1016/j.jcrysgro.2006.10.254.

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18

Sieber, J. "Generic stabilizability for time-delayed feedback control." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2189 (2016): 20150593. http://dx.doi.org/10.1098/rspa.2015.0593.

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Time-delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment. This approach feeds back only terms that depend on the difference between the current output and the output from a fixed time T ago. Thus, any periodic orbit of period T in the feedback-controlled system is also a periodic orbit of the uncontrolled system, independent of any modelling assumptions. It has been an open problem whether this approach can be successful in general, that is, under genericity conditions similar to those in linear control

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19

LI, P., Y. Z. LIU, K. L. HU, B. H. WANG, and H. J. QUAN. "THE CHAOTIC CONTROL ON THE OCCASIONAL NONLINEAR TIME-DELAYED FEEDBACK." International Journal of Modern Physics B 18, no. 17n19 (2004): 2680–85. http://dx.doi.org/10.1142/s0217979204025907.

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The method of controlling chaos by occasional nonlinear time-delayed feedback is proposed. Through the numerical analysis of bifurcation diagram and Lyapunov exponent, we found that the systematic chaos can be controlled effectively by the nonlinear time-delayed feedback as the form of u(xn,xn-k)=cxnxn-k. Under the proper feedback coefficient c, time-delayed coefficient k and occasional feedback period N, the system could be controlled from chaos to the steady periodic orbit, and also the steady period is the integral multiple of the occasional feedback period N.

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20

Pyragas, Kestutis. "Delayed feedback control of chaos." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 364, no. 1846 (2006): 2309–34. http://dx.doi.org/10.1098/rsta.2006.1827.

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Time-delayed feedback control is well known as a practical method for stabilizing unstable periodic orbits embedded in chaotic attractors. The method is based on applying feedback perturbation proportional to the deviation of the current state of the system from its state one period in the past, so that the control signal vanishes when the stabilization of the target orbit is attained. A brief review on experimental implementations, applications for theoretical models and most important modifications of the method is presented. Recent advancements in the theory, as well as an idea of using an

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21

Lehnert, J., P. Hövel, V. Flunkert, P. Yu Guzenko, A. L. Fradkov, and E. Schöll. "Adaptive tuning of feedback gain in time-delayed feedback control." Chaos: An Interdisciplinary Journal of Nonlinear Science 21, no. 4 (2011): 043111. http://dx.doi.org/10.1063/1.3647320.

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22

GUAN, XINPING, CAILIAN CHEN, HAIPENG PENG, and ZHENGPING FAN. "TIME-DELAYED FEEDBACK CONTROL OF TIME-DELAY CHAOTIC SYSTEMS." International Journal of Bifurcation and Chaos 13, no. 01 (2003): 193–205. http://dx.doi.org/10.1142/s021812740300642x.

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This paper addresses time-delayed feedback control (DFC) of time-delay chaotic systems. To extend the DFC approach to time-delay chaotic system, alter having been successfully used in chaotic systems without time-delays, the standard feedback control (SFC) method is firstly employed to show the main control technique in this paper based on one error control system. Then sufficient conditions for stabilization and tracking problems via DFC are derived from the results based on SFC. Also, the systematic and analytic controller design method can be obtained to stabilize the system to an unstable

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23

CHEN, GUANRONG, JIALIANG LU, BRENT NICHOLAS, and SWATIPRAKASH M. RANGANATHAN. "BIFURCATION DYNAMICS IN CONTROL SYSTEMS." International Journal of Bifurcation and Chaos 09, no. 01 (1999): 287–93. http://dx.doi.org/10.1142/s021812749900016x.

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This paper is to report the observation that when the popular time-delayed feedback strategy is used for control purpose, it may actually create unwanted bifurcations. Hopf bifurcation created by delayed feedback control is the main concern of this article, but some other types of bifurcations are also observed to exist in such delayed-feedback control systems. The observations are illustrated by computer simulations.

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24

Peng, Jian, Mingjiao Xiang, Luxin Li, Hongxin Sun, and Xiuyong Wang. "Time-Delayed Feedback Control of Piezoelectric Elastic Beams under Superharmonic and Subharmonic Excitations." Applied Sciences 9, no. 8 (2019): 1557. http://dx.doi.org/10.3390/app9081557.

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The time-delayed displacement feedback control is provided to restrain the superharmonic and subharmonic response of the elastic support beams. The nonlinear equations of the controlled elastic beam are obtained with the help of the Euler–Bernoulli beam principle and time-delayed feedback control strategy. Based on Galerkin method, the discrete nonlinear time-delayed equations are derived. Using the multiscale method, the first-order approximate solutions and stability conditions of three superharmonic and 1/3 subharmonic resonance response on controlled beams are derived. The influence of tim

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25

Guanrong Chen and Xinghuo Yu. "On time-delayed feedback control of chaotic systems." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 46, no. 6 (1999): 767–72. http://dx.doi.org/10.1109/81.768837.

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26

Zakharova, Anna, Nadezhda Semenova, Vadim Anishchenko, and Eckehard Schöll. "Time-delayed feedback control of coherence resonance chimeras." Chaos: An Interdisciplinary Journal of Nonlinear Science 27, no. 11 (2017): 114320. http://dx.doi.org/10.1063/1.5008385.

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27

Chatterjee, S. "Time-delayed feedback control of friction-induced instability." International Journal of Non-Linear Mechanics 42, no. 9 (2007): 1127–43. http://dx.doi.org/10.1016/j.ijnonlinmec.2007.08.002.

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28

Chatterjee, S. "Vibration control by recursive time-delayed acceleration feedback." Journal of Sound and Vibration 317, no. 1-2 (2008): 67–90. http://dx.doi.org/10.1016/j.jsv.2008.03.020.

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29

Fichtner, Andreas, Wolfram Just, and Günter Radons. "Analytical investigation of modulated time-delayed feedback control." Journal of Physics A: Mathematical and General 37, no. 10 (2004): 3385–91. http://dx.doi.org/10.1088/0305-4470/37/10/005.

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30

Sipahi, Rifat, and Nejat Olgac. "Active Vibration Suppression With Time Delayed Feedback." Journal of Vibration and Acoustics 125, no. 3 (2003): 384–88. http://dx.doi.org/10.1115/1.1569942.

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Various active vibration suppression techniques, which use feedback control, are implemented on the structures. In real application, time delay can not be avoided especially in the feedback line of the actively controlled systems. The effects of the delay have to be thoroughly understood from the perspective of system stability and the performance of the controlled system. Often used control laws are developed without taking the delay into account. They fulfill the design requirements when free of delay. As unavoidable delay appears, however, the performance of the control changes. This work a

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31

XU, XU, JIAWEI LUO, and YUANTONG GU. "COLLECTIVE DYNAMICS AND CONTROL OF A 3-D SMALL-WORLD NETWORK WITH TIME DELAYS." International Journal of Bifurcation and Chaos 22, no. 11 (2012): 1250281. http://dx.doi.org/10.1142/s0218127412502811.

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The paper presents a detailed analysis on the collective dynamics and delayed state feedback control of a three-dimensional delayed small-world network. The trivial equilibrium of the model is first investigated, showing that the uncontrolled model exhibits complicated unbounded behavior. Then three control strategies, namely a position feedback control, a velocity feedback control, and a hybrid control combined velocity with acceleration feedback, are then introduced to stabilize this unstable system. It is shown in these three control schemes that only the hybrid control can easily stabilize

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32

Wen, Shaofang, Yongjun Shen, Jiangchuan Niu, and Yunfei Liu. "Dynamical Behavior of Fractional-Order Delayed Feedback Control on the Mathieu Equation by Incremental Harmonic Balance Method." Shock and Vibration 2022 (July 19, 2022): 1–13. http://dx.doi.org/10.1155/2022/7515080.

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In this study, the dynamical analysis of the Mathieu equation with multifrequency excitation under fractional-order delayed feedback control is investigated by the incremental harmonic balance method (IHBM). IHBM is applied to the fractional-order delayed feedback control system, and the general formulas of the first-order approximate periodic solution for the Mathieu equation are derived. Caputo’s definition is adopted to process the fractional-order delayed feedback term. The general formulas of this system are suitable for not only the weakly but also the strongly nonlinear fractional-order

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33

Su, Huan, and Jing Xu. "Time-Delayed Sampled-Data Feedback Control of Differential Systems Undergoing Hopf Bifurcation." International Journal of Bifurcation and Chaos 31, no. 01 (2021): 2150004. http://dx.doi.org/10.1142/s0218127421500048.

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In this paper, time-delayed sampled-data feedback control technique is used to asymptotically stabilize a class of unstable delayed differential systems. Through the analysis for the distribution change of eigenvalues, an effective interval of the control parameter is obtained for a given sampling period. Here an indirect strategy is taken. Specifically, the system of continuous-time delayed feedback control is studied first by Hopf bifurcation theory. And then, the result and implicit function theorem are used to analyze the system of time-delayed sampled-data feedback control with a sufficie

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34

Just, Wolfram, Dirk Reckwerth, Ekkehard Reibold, and Hartmut Benner. "Influence of control loop latency on time-delayed feedback control." Physical Review E 59, no. 3 (1999): 2826–29. http://dx.doi.org/10.1103/physreve.59.2826.

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35

TIAN, YU-PING, XINGHUO YU, and LEON O. CHUA. "TIME-DELAYED IMPULSIVE CONTROL OF CHAOTIC HYBRID SYSTEMS." International Journal of Bifurcation and Chaos 14, no. 03 (2004): 1091–104. http://dx.doi.org/10.1142/s0218127404009612.

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This paper presents a time-delayed impulsive feedback approach to the problem of stabilization of periodic orbits in chaotic hybrid systems. The rigorous stability analysis of the proposed method is given. Using the time-delayed impulsive feedback method, we analyze the problem of detecting various periodic orbits in a special class of hybrid system, a switched arrival system, which is a prototype model of many manufacturing systems and computer systems where a large amount of work is processed in a unit time. We also consider the problem of stabilization of periodic orbits of chaotic piecewis

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36

WANG, ZAIHUA, and HAIYAN HU. "HOPF BIFURCATION CONTROL OF DELAYED SYSTEMS WITH WEAK NONLINEARITY VIA DELAYED STATE FEEDBACK." International Journal of Bifurcation and Chaos 15, no. 05 (2005): 1787–99. http://dx.doi.org/10.1142/s0218127405012909.

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This paper presents a study on the problem of Hopf bifurcation control of time delayed systems with weak nonlinearity via delayed feedback control. It focusses on two control objectives: one is to annihilate the periodic solution, namely to perform a linear delayed feedback control so that the trivial equilibrium is asymptotically stable, and the other is to obtain an asymptotically stable periodic solution with given amplitude via linear or nonlinear delayed feedback control. On the basis of the averaging method and the center manifold reduction for delayed differential equations, an effectiv

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37

Zhu, Erxi. "Time-delayed feedback control for chaotic systems with coexisting attractors." AIMS Mathematics 9, no. 1 (2023): 1088–102. http://dx.doi.org/10.3934/math.2024053.

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<abstract><p>This study investigated the Hopf bifurcation of the equilibrium point of chaotic systems with coexisting attractors under the time-delayed feedback control. First, the equilibrium point and Hopf bifurcation of chaotic systems with coexisting attractors were analyzed. Second, the chaotic systems were controlled by time-delayed feedback, the transversality condition of Hopf bifurcation at the equilibrium point was discussed, and the time-delayed value of Hopf bifurcation at the equilibrium point was obtained. Lastly, the correctness of the theoretical analysis was verifi

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38

Rezaie, Behrooz, and Mohammad-Reza Jahed Motlagh. "An adaptive delayed feedback control method for stabilizing chaotic time-delayed systems." Nonlinear Dynamics 64, no. 1-2 (2010): 167–76. http://dx.doi.org/10.1007/s11071-010-9855-7.

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Guo, Yong, Yuh-Chung Hu, and Chuan-Bo Ren. "An Optimization Algorithm of Time-Delayed Feedback Control Parameters for Quarter Vehicle Semiactive Suspension System." Mathematical Problems in Engineering 2022 (April 30, 2022): 1–9. http://dx.doi.org/10.1155/2022/2946091.

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Time-delayed feedback control is commonly used on the vehicle semiactive suspension system to improve ride comfort and safety. However, its performance on the suppression of road random excitation is less significant than that on the suppression of simple harmonic excitation. Therefore, this paper proposes a strategy of time-delayed feedback control with the vertical displacement of wheel and the method of optimizing its parameters based on equivalent harmonic excitation. The optimal parameters of the time-delayed feedback control are obtained in this way for the vehicle semiactive suspension

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40

Schneider, Isabelle, and Matthias Bosewitz. "Eliminating restrictions of time-delayed feedback control using equivariance." Discrete and Continuous Dynamical Systems 36, no. 1 (2015): 451–67. http://dx.doi.org/10.3934/dcds.2016.36.451.

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41

Semenov, V. V., T. E. Vadivasova, E. Schöll, and A. S. Zakharova. "Time-delayed Feedback Control of Coherence Resonance. Experimental Study." Series Physics 15, no. 3 (2015): 43–51. http://dx.doi.org/10.18500/1817-3020-2015-15-3-43-51.

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42

Schneider, F. W., R. Blittersdorf, A. Foerster, T. Hauck, D. Lebender, and J. Mueller. "Continuous control of chemical chaos by time delayed feedback." Journal of Physical Chemistry 97, no. 47 (1993): 12244–48. http://dx.doi.org/10.1021/j100149a025.

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43

Yang Ru and Zhang Bo. "Chaotification control of buck converter via time-delayed feedback." Acta Physica Sinica 56, no. 7 (2007): 3789. http://dx.doi.org/10.7498/aps.56.3789.

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44

Zhang, Shu, and Jian Xu. "Time-varying delayed feedback control for an internet congestion control model." Discrete & Continuous Dynamical Systems - B 16, no. 2 (2011): 653–68. http://dx.doi.org/10.3934/dcdsb.2011.16.653.

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45

Stavrinides, S. G., M. P. Hanias, L. Magafas, and S. Banerjee. "Control of Economic Situations by Utilizing an Electronic Circuit." International Journal of Productivity Management and Assessment Technologies 3, no. 2 (2015): 1–15. http://dx.doi.org/10.4018/ijpmat.2015070101.

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In this paper a circuit (physical system), implementing a financial system with time-delayed feedbacks, is designed and studied. The simple form of this dynamical system, without any time-delayed feed, has been already investigated and was found to demonstrate both a periodic and chaotic behavior. By introducing the time-delayed feedback, according to the Pyragas method, control of the circuit's-system's chaotic behaviour could be achieved. Its overall operation was simulated, using NI's Multisim and control of its behaviour was achieved by controlling feedback delay-time of a certain system v

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46

MORGÜL, ÖMER. "A NEW GENERALIZATION OF DELAYED FEEDBACK CONTROL." International Journal of Bifurcation and Chaos 19, no. 01 (2009): 365–77. http://dx.doi.org/10.1142/s0218127409022920.

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In this paper, we consider the stabilization problem of unstable periodic orbits of one-dimensional discrete time chaotic systems. We propose a novel generalization of the classical delayed feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized by the proposed method; for higher order periods the proposed scheme possesses some inherent limitations. However, some more improvement over the classical delayed feedback scheme can be achieved with the proposed scheme. The stability proofs also give the possible feedback

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47

Ahn, Choon Ki. "Fuzzy delayed output feedback synchronization for time-delayed chaotic systems." Nonlinear Analysis: Hybrid Systems 4, no. 1 (2010): 16–24. http://dx.doi.org/10.1016/j.nahs.2009.07.002.

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Nestler, Peter, Eckehard Schöll, and Fredi Tröltzsch. "Optimization of nonlocal time-delayed feedback controllers." Computational Optimization and Applications 64, no. 1 (2015): 265–94. http://dx.doi.org/10.1007/s10589-015-9809-6.

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Wang, Huailei, and Guanrong Chen. "On the initial function space of time-delayed systems: A time-delayed feedback control perspective." Journal of the Franklin Institute 352, no. 8 (2015): 3243–49. http://dx.doi.org/10.1016/j.jfranklin.2014.10.021.

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Vasegh, Nastaran, and Ali Khaki Sedigh. "Delayed feedback control of time-delayed chaotic systems: Analytical approach at Hopf bifurcation." Physics Letters A 372, no. 31 (2008): 5110–14. http://dx.doi.org/10.1016/j.physleta.2008.06.023.

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