非线性系统的实现与最小阶问题
Realization and Minimal Order for Nonlinear Systems
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摘要: 在系统的微分域及相应的微分向量空间上定义了一个非交换的多项式环(算子环), 并利用这个环定义非线性系统的传递函数.用微分向量空间为工具,讨论单输入/单输出非线 性系统的实现问题.主要结果回答了:1)在什么条件下,不同的输入/输出微分方程有相同(等 价)的实现;2)在未知实现的条件下,如何确定输入/输出微分方程最小实现的阶数.覆盖了线 性系统理论的相关结果.Abstract: The realization problems for single-input/single-output differential equations are discussed within the framework of differential vector space .fain results of this work answer two fundamental questions: (1) under what conditions different input/output differential equations have the same realization; (2)how to calculate the order of the minimal realization of input/output differential equations without knowing its realization. In order to solve these problems the notion of transfer function for nonlinear systems is defined over a non-commutative polynomial ring. The description of nonlinear realization problems is fully incorporated with that of the linear control theory.
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Key words:
- Nonlinear system /
- realization /
- differential vector space /
- non-commutative ring /
- transfer function
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