Orders of Input/Output Differential Equations and State-Space Dimensions
Orders of Input/Output Differential Equations and State-Space Dimensions
复制标题
输入/输出微分方程的阶数和状态空间维数
DOI：
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发表时间：
1995
期刊：
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通讯作者：
Eduardo Sontag
中科院分区：
文献类型：
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作者：
Y. Wang;Eduardo Sontag
本文讨论了非线性系统所满足的输入输出方程的阶数。这些方程分别表示输入和输出信号的高阶导数(或移位)之间的微分(或在离散时间情况下为差)关系。结果表明，在解析性假设下，不可能存在低于任何可观测实现的最小维度的阶方程；这推广了经典线性情况下的已知情况。结果依赖于新的事实，这些事实本身在控制理论中引起了相当大的兴趣，涉及离散情况下可观测性的通用输入，以及离散和连续情况下的观测空间。文中还给出了连续时间分析系统的Sussmann通用输入定理的一个新的、简单的、完备的证明。
This paper deals with the orders of input/output equations satisfied by nonlinear systems. Such equations represent differential (or difference, in the discrete-time case) relations between high-order derivatives (or shifts, respectively) of input and output signals. It is shown that, under analyticity assumptions, there cannot exist equations of order less than the minimal dimension of any observable realization; this generalizes the known situation in the classical linear case. The results depend on new facts, themselves of considerable interest in control theory, regarding universal inputs for observability in the discrete case, and observation spaces in both the discrete and continuous cases. Included in the paper is also a new and simple self-contained proof of Sussmann's universal input theorem for continuous-time analytic systems.