Estimating the ultimate bound and positively invariant set for a synchronous motor and its application in chaos synchronization

Fuchen Zhang, Yonglu Shu, Hongliang Yang and Xiaowu Li

Chaos, Solitons & Fractals, 2011, vol. 44, issue 1, 137-144

Abstract: To estimate the ultimate bound and positively invariant set for a dynamic system is an important but quite challenging task in general. This paper has investigated the ultimate bound and positively invariant set of a permanent magnet synchronous motor system. We combine the Lyapunov stability theory with the comparison principle method. For this system, we derive a three-dimensional ellipsoidal ultimate bound and positively invariant set for all the positive values of its parameters σ, γ. In addition, the two-dimensional bound with respect to x−y are established. Then, it is the two-dimensional estimation about x−z. Finally, the result is applied to the study of completely chaos synchronization. Numerical simulations are presented to show the effectiveness of the proposed chaos synchronization scheme. At the same time, one numerical example illustrating a localization of a chaotic attractor is presented as well. Numerical simulation is consistent with the results of theoretical calculation.

Date: 2011
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:44:y:2011:i:1:p:137-144

DOI: 10.1016/j.chaos.2011.01.001

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