Absolute Stability Theory and the Synchronization Problem

Curran, Paul; Chua, Leon O.

doi:10.1142/s0218127497001096

Cited by 124 publications

(88 citation statements)

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“…While the synchronization can be manifested until the maximum delay h = 0.28 in [10], h = 0.213 in [21] and [7], h = 0.222 in [20], h > 0.25 in [8] respectively. This implies that our criterion is less conservative than that in [3] and [7,8,10,20,21]. e (t) = (A + ∆A (t)) e (t) + (B + ∆B (t)) η (Ce (t) , y (t)) − MHe (t − h (t)) , It is clear that the state trajectories approach to zero asymptotically.…”

Section: Examplesmentioning

confidence: 98%

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New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

Wang¹,

Xiong²,

Liu³

et al. 2017

J. Nonlinear Sci. Appl.

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This paper studies the problem of master-slave synchronization for uncertain Lur'e system via time-varying delayed feedback control. It proves a new inequality involving double integrals, which can reduce the conservatism of the known Jensen's like inequalities according to our analysis. By employing this new inequality and a new class of novel mode-dependent augmented Lyapunov-Krasovskii functional (LKF), it establishes some novel synchronization criteria, where the controller gain can be achieved by solving a set of linear matrix inequalities (LMIs). Two examples with numerical simulations are given to illustrate the feasibility and the superiority of our methods.

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Section: Examplesmentioning

confidence: 98%

“…Such synchronization has been widely explored in a variety of fields including physical, chemical and ecological systems, human heartbeat regulation, secure communications, and so on. Moreover, a number of master-slave synchronization schemes for Lur'e systems have been proposed [3,4,12,15,17,18].…”

Section: Introductionmentioning

confidence: 99%

New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

Wang¹,

Xiong²,

Liu³

et al. 2017

J. Nonlinear Sci. Appl.

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“…Consider the master-slave synchronization scheme with full static-state error feedback [21], [5], [17] (1) with master system slave system and controller The index refers to the static feedback case. The master and slave system are Lur'e systems with state vectors , respectively, and matrices and A Lur'e system is a linear dynamical system, feedback interconnected to a static nonlinearity that satisfies a sector condition [9], [20] (here it has been represented as a recurrent neural network with one hidden layer, activation function , and hidden units [15]).…”

Section: A Full Static-state Error Feedbackmentioning

confidence: 99%

“…M ASTER-SLAVE synchronization schemes for Lur'e systems have been studied in [5], [6], and [16] for the autonomous case with static-state feedback or dynamicoutput feedback applied to the slave system. With respect to secure communications applications [8], the nonautonomous case has been studied in [17] and [18] where an informationcarrying message signal is considered as an external input.…”

Section: Introductionmentioning

confidence: 99%

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Robust synthesis for master-slave synchronization of Lur'e systems

Suykens

Curran

Chua

1999

IEEE Trans. Circuits Syst. I

171

132

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Abstract-In this paper a method for robust synthesis of full static-state error feedback and dynamic-output error feedback for master-slave synchronization of Lur'e systems is presented. Parameter mismatch between the systems is considered in the synchronization schemes. Sufficient conditions for uniform synchronization with a bound on the synchronization error are derived, based on a quadratic Lyapunov function. The matrix inequalities from the case without parameter mismatch between the Lur'e systems remain preserved, but an additional robustness criterion must be taken into account. The robustness criterion is based on an uncertainty relation between the synchronization error bound and the parameter mismatch. The robust synthesis method is illustrated on Chua's circuit with the double scroll. One observes that it is possible to synchronize the master-slave systems up to a relatively small error bound, even in the case of different qualitative behavior between the master and the uncontrolled slave system, such as limit cycles and stable equilibria.

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Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

2014

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This article investigates the chaos control problem for the fractional‐order chaotic systems containing unknown structure and input nonlinearities. Two types of nonlinearity in the control input are considered. In the first case, a general continuous nonlinearity input is supposed in the controller, and in the second case, the unknown dead‐zone input is included. In each case, a proper switching adaptive controller is introduced to stabilize the fractional‐order chaotic system in the presence of unknown parameters and uncertainties. The control methods are designed based on the boundedness property of the chaotic system's states, where, in the proposed methods the nonlinear/linear dynamic terms of the fractional‐order chaotic systems are assumed to be fully unknown. The analytical results of the mentioned techniques are proved by the stability analysis theorem of fractional‐order systems and the adaptive control method. In addition, as an application of the proposed methods, single input adaptive controllers are adopted for control of a class of three‐dimensional nonlinear fractional‐order chaotic systems. And finally, some numerical examples illustrate the correctness of the analytical results. © 2014 Wiley Periodicals, Inc. Complexity 21: 211–223, 2015

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Absolute Stability Theory and the Synchronization Problem

Cited by 124 publications

References 0 publications

New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

New delay-dependent synchronization criteria for uncertain Lur'e systems via time-varying delayed feedback control

Robust synthesis for master-slave synchronization of Lur'e systems

Switching adaptive controllers to control fractional‐order complex systems with unknown structure and input nonlinearities

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