| Hybrid singular systems of differential equations |
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| 作者姓名： | 殷刚 张纪峰 |
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| 作者单位： | YIN Gang & ZHANG Jifeng1. Department of Mathematics，Wayne State University，Detroit，Ml 48202，USA;2. Institute of Systems Science，Academy of Mathematics and System Sciences，Chinese Academy of Sciences，Beijing，100080，China |
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| 基金项目： | Yin Gang was supported by the National Science Foundation of US (Grant No.
DMS-9877090)，and Zhang Jifeng was supported by the National Natural Science Foundation of China (Grant No. 69725006). |
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| 摘 要： | This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresponding dynamic systems is markedly different, our goals are to develop hybrid systems in which continuous dynamics are intertwined with discrete events under random-jump disturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markov chains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in the formulation. Under general assumptions, limit behavior of the underlying system is examined. Using weak convergence methods, it is shown that the systems can be approximated by limit systems in which the coefficients are averaged out with respect to the quasi-stationary distributions. Since the limit systems have fewer states, the complexity is much reduced.
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| 收稿时间： | 26 November 2000 |
Hybrid singular systems of differential equations |
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| Yin Gang,and Zhang Jifeng.Hybrid singular systems of differential equations[J].Science in China(Information Sciences),2002,45(4):241-258. |
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| Authors: | Yin Gang and Zhang Jifeng |
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| Affiliation: | 1. Department of Mathematics, Wayne State University, Detroit, MI 48202, USA
2. Institute of Systems Science, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing, 100080, China |
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| Abstract: | This work develops hybrid models for large-scale singular differential system and analyzes their asymptotic properties. To take into consideration the discrete shifts in regime across which the behavior of the corresponding dynamic systems is markedly different, our goals are to develop hybrid systems in which continuous dynamics are intertwined with discrete events under random-jump disturbances and to reduce complexity of large-scale singular systems via singularly perturbed Markov chains. To reduce the complexity of large-scale hybrid singular systems, two-time scale is used in the formulation. Under general assumptions, limit behavior of the underlying system is examined. Using weak convergence methods, it is shown that the systems can be approximated by limit systems in which the coefficients are averaged out with respect to the quasi-stationary distributions. Since the limit systems have fewer states, the complexity is much reduced. |
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| Keywords: | hybrid model singular system differential equation singularly perturbed Markov chain weak convergence averaging |
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