Expansion of solution of an inverted pendulum system with time delay |
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Authors: | Ya-Xuan ZhangZhong-Jie Han Gen-Qi Xu |
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Institution: | a College of Science, Civil Aviation University of China, Tianjin 300300, China b Department of Mathematics, Tianjin University, Tianjin 300072, China |
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Abstract: | In this paper, the solution expansion for an inverted pendulum system with time delay is studied. The linearized model of this nonlinear system near its equilibrium is derived on the assumption that a unique equilibrium exists in it. Then the asymptotic expressions of its eigenvalues and the eigenvalues’ corresponding eigenvectors are obtained. Moreover, although the set of these eigenvectors does not form a Schauder basis for the state space, the solution of this model still can be expressed by these eigenvectors in the form of infinite series under certain conditions. Finally, a simulation is provided to support these results. |
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Keywords: | Expansion Time delay Spectrum Eigenvector Semigroup Inverted pendulum |
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