Bounding a domain containing all compact invariant sets of the permanent-magnet motor system

Coria, Luis N.; Starkov, Konstantin E.

doi:10.1016/j.cnsns.2008.09.001

Cited by 29 publications

(16 citation statements)

References 25 publications

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“…And some results on the localization of all compact invariant sets of the system (2.1) are described as follows (see [28][29][30][31][32]). …”

Section: Some Notations and Preliminariesmentioning

confidence: 99%

“…Recently, an ultimate bound and positively invariant set for the hyperchaotic Lorenz-Haken system was obtained in [26], and Wang et al studied the boundedness for the hyper-chaotic Lorenz-Stenflo system in [27]. Coria and Starkov [28] considered the boundedness of a chaotic system with the help of iterative theory. By applying a similar method, in [29][30][31][32][33], they studied the boundedness of other chaotic systems.…”

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confidence: 98%

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On the boundedness of solutions to the Lorenz-like family of chaotic systems

Zhang

Shu

et al. 2011

Nonlinear Dyn

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This paper deals with a class of threedimensional autonomous nonlinear systems which have potential applications in secure communications, and investigates the localization problem of compact invariant sets of a class of Lorenz-like chaotic systems which contain T system with the help of iterative theorem and Lyapunov function theorem. Since the Lorenz-like chaotic system does not have y in the second equation, the approach used to the Lorenz system cannot be applied to the Lorenz-like chaotic system. We overcome this difficulty by introducing a cross term and get an interesting result, which includes the most interesting case of the chaotic attractor of the Lorenz-like systems. Furthermore, the results obtained in this paper are applied to study complete chaos synchronization. Finally, numerical simulations show the effectiveness of the proposed scheme.

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“…And some results on the localization of all compact invariant sets of the system (2.1) are described as follows (see [28][29][30][31][32]). …”

Section: Some Notations and Preliminariesmentioning

confidence: 99%

mentioning

confidence: 98%

On the boundedness of solutions to the Lorenz-like family of chaotic systems

Zhang

Shu

et al. 2011

Nonlinear Dyn

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“…HAOS, as a very interesting nonlinear phenomenon with complex behavior, has been intensively studied in the last decades [1][2][3][4][5][6][7][8][9][10][11]. Meanwhile, a chaotic system is bounded, in the sense that its chaotic attractor is bounded in the phase space, and the estimate of its bound is important for the study of the qualitative behavior of a chaotic system, such as chaos control, chaos synchronization and their applications.…”

Section: Introductionmentioning

confidence: 99%

“…This greatly simplifies the analysis of dynamics of the system. And recently, many chaotic system, such as the Lorenz system [1], the Chen system [2], the Qi chaotic system [3], the general lorenz-type new chaotic systems [4], the hyperchaotic Lorenz-Haken system [5], the chaotic finance system [6] and the permanent magnet synchronous motor (PMSM) [7], the ultimate boundedness property for these chaotic systems has been investigated by many researchers. For the Hadley system, the results of detailed estimations of ultimate boundedness for the Hadley system has not been considered, the paper [8] has proofed that the Hadley system is bounded, but where detailed formulas of the bounded estimate were not given,.…”

Section: Introductionmentioning

confidence: 99%

Estimations of bounds and synchronization controlling for Hadley chaotic system

Zhao

Jian

Wang

2012

2012 IEEE International Conference on Information Science and Technology

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This paper is concerned with positive invariant set and synchronization controlling for Hadley chaotic system. A detailed spheroid estimation of the globally exponentially attractive set is derived for the Hadley chaotic system. In addition, linear feedback control with two inputs is proposed to realize the globally exponential synchronization of two Hadley chaotic systems based on matrix theory. New sufficient algebraic criteria for the globally exponential synchronization of two Hadley chaotic systems are obtained analytically. The controllers here designed have simple structure and less conservation. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme.

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“…It is well known that the existing mathematical models of generators are multi-variable, nonlinear, and strongly coupled; therefore, these systems can exhibit complex behaviors [8][9][10][11]. It is now a common belief that understanding and utilizing the rich dynamics, such as bifurcations and chaos, of nonlinear systems have an important impact on the modern technology [12][13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

A Novel Method to Magnetic Flux Linkage Optimization of Direct-Driven Surface-Mounted Permanent Magnet Synchronous Generator Based on Nonlinear Dynamic Analysis

Zhang

et al. 2016

Energies

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This paper pays attention to magnetic flux linkage optimization of a direct-driven surface-mounted permanent magnet synchronous generator (D-SPMSG). A new compact representation of the D-SPMSG nonlinear dynamic differential equations to reduce system parameters is established. Furthermore, the nonlinear dynamic characteristics of new D-SPMSG equations in the process of varying magnetic flux linkage are considered, which are illustrated by Lyapunov exponent spectrums, phase orbits, Poincaré maps, time waveforms and bifurcation diagrams, and the magnetic flux linkage stable region of D-SPMSG is acquired concurrently. Based on the above modeling and analyses, a novel method of magnetic flux linkage optimization is presented. In addition, a 2 MW D-SPMSG 2D/3D model is designed by ANSYS software according to the practical design requirements. Finally, five cases of D-SPMSG models with different magnetic flux linkages are simulated by using the finite element analysis (FEA) method. The nephograms of magnetic flux density are agreement with theoretical analysis, which both confirm the correctness and effectiveness of the proposed approach.

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Bounding a domain containing all compact invariant sets of the permanent-magnet motor system

Cited by 29 publications

References 25 publications

On the boundedness of solutions to the Lorenz-like family of chaotic systems

On the boundedness of solutions to the Lorenz-like family of chaotic systems

Estimations of bounds and synchronization controlling for Hadley chaotic system

A Novel Method to Magnetic Flux Linkage Optimization of Direct-Driven Surface-Mounted Permanent Magnet Synchronous Generator Based on Nonlinear Dynamic Analysis

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