System theory for numerical analysis
| Authors: | Kenji Kashima, Kyoto University, Japan
Ashida Shinjiro, Kyoto University, Japan
Yamamoto Yutaka, Kyoto University, Japan |
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| Topic: | 2.1 Control Design |
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| Session: | Numerical Issues in Systems and Control |
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| Keywords: | Numerical Analysis, System theory, Newton’s method, Runge-Kutta type method, Absolute stability, Generalized Kalman-Yakubovich-Popov lemma |
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Abstract
System theory for numerical analysis has recently become a focus ofresearch. In this paper we regard dynamics of Newton’s method as a nonlinearfeedback system and derive convergence conditions, based on the internal modelprinciple and systems of Lur’e type. We then focus our attention on the analysisof the region of absolute stability of Runge-Kutta type methods. We derivea linear matrix inequality condition which characterizes a relationship betweenRunge-Kutta coefficients and the corresponding stability region. We also proposea new optimization procedure for designing a Runge-Kutta method based on thischaracterization.
