Realization and Structure Theory of Bilinear Dynamical Systems
Realization and Structure Theory of Bilinear Dynamical Systems
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DOI：
10.1137/0312040
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发表时间：
1974-08
期刊：
影响因子：
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通讯作者：
P. d'Alessandro;A. Isidori;A. Ruberti
中科院分区：
文献类型：
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作者：
P. d'Alessandro;A. Isidori;A. Ruberti
本文从零态响应级数展开提供的系统描述出发，发展了双线性系统的实现理论。结果表明，可实现性的条件与该展开式的核的可分解性的条件相对应。然后本文分析了最小因式分解和非最小因式分解的性质，并提供了表征最小实现的问题的解决方案。随后，开展了状态空间的结构分析，证明了方程组存在规范形式，并在此基础上解释了实现理论的结果。最后，为开发实现程序奠定了基础，并证明了双线性系统的核序列完全可以由有限数量的核来辨识。
Starting from the description of the system provided by the series expansion of the zero-state response, this paper develops the realization theory for bilinear systems. It is shown that the condition of realizability corresponds to that of the factorizability of the kernels of this expansion. The paper then analyzes the properties of the minimal and nonminimal factorizations and provides a solution of the problem of characterizing the minimal realizations. Subsequently, developing the structure analysis of the state space, it is shown that there exists a canonical form of the equations and the results of the realization theory are interpreted on this basis. Lastly, the bases are laid for developing realization procedures, and it is shown that the sequence of kernels of a bilinear system is completely identified by a finite number of these kernels.