Solution bounds of a new complex PMSM system
This paper has investigated the boundedness of solutions of a complex permanent magnet synchronous motor system. We have obtained the globally exponentially attractive set Ψ λ,m and the ultimate bound Ω λ,m for this system. Furthermore, we can conclude that the rate of the trajectories of the system going from the exterior of the set Ψ λ,m to the interior of the set Ψ λ,m is exponential. The estimate of the trajectories rate is also obtained. Numerical simulations are presented to show the effectiveness of the proposed scheme.
KeywordsComplex PMSM chaotic system Globally exponentially attractive set Generalized Lyapunov function
This work is supported in part by the Fundamental Research Funds for the Central Universities (No. CDJXS11100026) and in part by NSF of P.R. China (No. 11071266, No. 61173183). We would like to thank the reviewers and editors for their valuable comments and suggestions and their time and efforts to review the manuscript. Without their constructive comments, the paper would not be of current quality. We also thank Gaoxiang Yang at the Department of Mathematics and Statistics of Ankang University for his help.
- 16.Liao, X.: On the global basin of attraction and positively invariant set for the Lorenz chaotic system and its application in chaos control and synchronization. Sci. China Ser. E 34(12), 1404–1419 (2004) Google Scholar
- 17.Chen, G., Lü, J.: Dynamical Analysis, Control and Synchronization of the Lorenz Systems Family. Science Press, Beijing (2003) Google Scholar
- 29.Lefchetz, S.: Differential Equations: Geometric Theory. Interscience, New York (1963) Google Scholar