Existence and uniqueness of minimal realizations of nonlinear systems
Existence and uniqueness of minimal realizations of nonlinear systems
复制标题
非线性系统最小实现的存在唯一性
DOI：
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
H. Sussmann
中科院分区：
文献类型：
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作者：
H. Sussmann
在有限维线性系统的理论中，众所周知，可以由一个这样的系统实现的每个输入-输出映射也可以由“最小”系统实现，即既可控又可观测。此外，一个给定的映射的最小实现是唯一的同构。这里表明，类似的结果持有的所有系统的状态空间是一个真实的解析流形，其动力学是由一个家庭的完整的真实的解析向量场，其输出是一个任意的真实的解析函数的状态空间的类。
In the theory of finite dimensional linear systems, it is well known that every input-output map that can be realized by one such system can also be realized by a system which is “minimal”, i.e. both controllable and observable. Moreover, the minimal realization of a given map is unique up to isomorphism. It is shown here that similar results hold for the class of all systems whose state space is a real analytic manifold, whose dynamics is given by a family of complete real analytic vector fields, and whose output is an arbitrary real analytic function on the state space.